TRG2.ipynb

{
 "cells": [
  {
   "cell_type": "code",
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   "source": [
    "# -*- coding: utf-8 -*-\n",
    "\"\"\" \n",
    "mainTRG.py\n",
    "---------------------------------------------------------------------\n",
    "Script file for initializing a partition function (here the classical \\\n",
    "Ising model) before passing to a Tensor Renormalization Group (TRG) \\\n",
    "coarse-graining routine. The magnetization, free energy and internal \\\n",
    "energy are then computed and compared against the exact results.\n",
    "\n",
    "by Glen Evenbly (c) for www.tensors.net, (v1.1) - last modified 26/1/2019\n",
    "\"\"\"\n",
    "\n",
    "#### Preamble\n",
    "import numpy as np\n",
    "from numpy import linalg as LA\n",
    "\n",
    "from ncon import ncon\n",
    "from doTRG import doTRG \n",
    "\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "def iterTRG(numlevels, Tval):\n",
    "    ##### Example 1: square lattice classical Ising model #####\n",
    "    ###########################################################\n",
    "\n",
    "    ##### Set bond dimensions and temperature\n",
    "    chiM = 32\n",
    "    chiH = 32\n",
    "    chiV = 32\n",
    "    \n",
    "    OPTS_midsteps = 10 # iterations in isometry optimization\n",
    "\n",
    "    ##### Define partition function (classical Ising)\n",
    "    \n",
    "    betaval = 1/Tval\n",
    "    Jtemp = np.zeros((2,2,2)); Jtemp[0,0,0]=1; Jtemp[1,1,1]=1\n",
    "    Etemp = np.array([[np.exp(betaval),np.exp(-betaval)],[np.exp(-betaval),np.exp(betaval)]])\n",
    "\n",
    "    Ainit = ncon([Jtemp,Jtemp,Jtemp,Jtemp,Etemp,Etemp,Etemp,Etemp],\n",
    "             [[-1,8,1],[-2,2,3],[-3,4,5],[-4,6,7],[1,2],[3,4],[5,6],[7,8]])\n",
    "    Atemp = Ainit.reshape(2,2,2,2)\n",
    "\n",
    "    Anorm = [0 for x in range(numlevels+1)]\n",
    "    Anorm[0] = LA.norm(Atemp.flatten())\n",
    "    A = [0 for x in range(numlevels+1)]\n",
    "    A[0] = Atemp/Anorm[0]\n",
    "\n",
    "    ##### Do iterations of TRG\n",
    "    SPerrs = np.zeros((numlevels,3))\n",
    "    qC = [0 for x in range(numlevels)]\n",
    "    vC = [0 for x in range(numlevels)]\n",
    "    wC = [0 for x in range(numlevels)]\n",
    "    for k in range(numlevels):\n",
    "        A[k+1], qC[k], vC[k], wC[k], Anorm[k+1], SPerrs[k,:] = doTRG(A[k],chiM,chiH,chiV, midsteps = OPTS_midsteps)\n",
    "        #print('RGstep: %d, Truncation Errors: %e, %e, %e' % (k,SPerrs[k,0],SPerrs[k,1],SPerrs[k,2]))\n",
    "    return A, vC, wC, Anorm\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "\"\"\"\n",
    "evalTRG: evaluates outputs from TNR algorithm to compute several \\\n",
    "quantities for the Ising model (free energy, internal energy)\n",
    "\"\"\"\n",
    "def evalTRG(numlevels, Tval, A, vC, wC, Anorm):\n",
    "\n",
    "    ##### Evaluate free energy density as a function of system size\n",
    "    NumSpins = 2**(2*np.int64(np.array(range(20)))+1)\n",
    "    FreeEnergy = np.zeros(numlevels);\n",
    "    for k in range(1,numlevels+1): \n",
    "        FreeEnergy[k-1] = -Tval*(sum((4**np.int64(np.array(range(k,-1,-1))))*np.log(Anorm[:(k+1)])) +\n",
    "                  np.log(ncon([A[k]],[[1,2,1,2]]))) / NumSpins[k]\n",
    "\n",
    "    ##### Evaluate local density matrix, internal energy, spontaneous mag\n",
    "    maglambda = 1/(np.sinh(2/Tval)**2) # mag field (quantum Ising) from temp (classical Ising)\n",
    "    betaval = 1/Tval\n",
    "\n",
    "    sX = np.array([[1, 0], [0,-1]])\n",
    "    sXsX = np.kron(sX,sX).reshape(2,2,2,2) # spin1 - 1,3; spin2 - 2,4\n",
    "\n",
    "\n",
    "    sXcg = [0 for x in range(numlevels+1)]\n",
    "    sXcg[0] = sX\n",
    "\n",
    "    sXsXcgtemp = [0 for x in range(numlevels+1)]\n",
    "    sXsXcgtemp[0] = sXsX\n",
    "\n",
    "    ExpectXX = [0 for x in range(numlevels-1)]\n",
    "\n",
    "    base = ncon([A[numlevels]],[[1,2,1,2]])\n",
    "    #print('base: ', base)\n",
    "\n",
    "    for k in range(numlevels):\n",
    "        sXcg[k+1] = ncon([sXcg[k],wC[k],wC[k]],[[1,2],[1,3,-1],[2,3,-2]])\n",
    "    \n",
    "    for x in range(numlevels-1):\n",
    "        sXsXcgtemp[x+1] = ncon([sXsXcgtemp[x],vC[x],vC[x]],[[1,2,3,4],[1,2,-1],[3,4,-2]])\n",
    "        \n",
    "        for k in range(x+1, numlevels): \n",
    "            sXsXcgtemp[k+1] = ncon([sXsXcgtemp[k],vC[k],vC[k]],[[1,2],[1,3,-1],[2,3,-2]])\n",
    "\n",
    "        cal = ncon([A[numlevels], sXsXcgtemp[numlevels]],[[1,2,3,2],[1,3]])\n",
    "\n",
    "        sXsXcgtemp[x+1] = ncon([sXsXcgtemp[x],vC[x],vC[x],vC[x],vC[x]],[[1,2,3,4],[1,5,-1],[3,5,-3],[2,6,-2],[4,6,-4]])\n",
    "    \n",
    "        #print('cal: ', cal)\n",
    "        ExpectXX[x] = cal/base\n",
    "    \n",
    "    dtemp = LA.eigvalsh(sXcg[numlevels])\n",
    "    ExpectX = max(abs(dtemp))\n",
    "    \n",
    "    ##### Compare with exact results (thermodynamic limit)\n",
    "    N = 1000000\n",
    "    x = np.linspace(0,np.pi,N+1)\n",
    "    y = np.log(np.cosh(2*betaval)*np.cosh(2*betaval) + (1/maglambda)*np.sqrt(\n",
    "            1+maglambda**2 -2*maglambda*np.cos(2*x)))\n",
    "    FreeExact = -Tval*((np.log(2)/2) + 0.25*sum(y[1:(N+1)] + y[:N])/N)\n",
    "    \n",
    "    ExpectXExact = 0\n",
    "    if maglambda < 1:\n",
    "        ExpectXExact = (1 - np.sinh(2*betaval)**(-4))**(1/8)\n",
    "    \n",
    "    return FreeEnergy[numlevels-1], FreeExact, ExpectX, ExpectXExact, ExpectXX"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Tenperature: 0.022692, FreeEnergy: -2.000000, FreeExact: -2.000000, ExpectX: 1.000000, ExpectXExact: 1.000000\n",
      "ExpectXX:  [1.0000000000000018, 1.0000000000000018, 1.0000000000000022, 1.0000000000000029, 1.000000000000003, 1.000000000000004, 1.0000000000000036, 1.0000000000000044, 1.0000000000000042, 1.0000000000000038, 1.000000000000005, 1.000000000000004, 1.0000000000000044, 1.0000000000000044, 1.0000000000000044]\n",
      "Tenperature: 0.114849, FreeEnergy: -2.000000, FreeExact: -2.000000, ExpectX: 1.000000, ExpectXExact: 1.000000\n",
      "ExpectXX:  [1.0000000000000018, 1.0000000000000024, 1.0000000000000024, 1.0000000000000022, 1.0000000000000022, 1.0000000000000013, 1.0000000000000018, 1.0000000000000024, 1.0000000000000018, 1.0000000000000022, 1.000000000000003, 1.0000000000000029, 1.000000000000003, 1.0000000000000038, 1.0000000000000033]\n",
      "Tenperature: 0.207005, FreeEnergy: -2.000000, FreeExact: -2.000000, ExpectX: 1.000000, ExpectXExact: 1.000000\n",
      "ExpectXX:  [1.0000000000000009, 1.000000000000001, 1.0000000000000002, 1.0000000000000002, 0.9999999999999999, 1.0000000000000002, 1.0000000000000002, 1.0000000000000009, 1.000000000000001, 1.0000000000000013, 1.0000000000000018, 1.0000000000000022, 1.000000000000001, 1.0000000000000018, 1.0000000000000013]\n",
      "Tenperature: 0.299162, FreeEnergy: -2.000000, FreeExact: -2.000000, ExpectX: 1.000000, ExpectXExact: 1.000000\n",
      "ExpectXX:  [0.9999999999902656, 0.9999999999902652, 0.9999999999902656, 0.9999999999902663, 0.9999999999902662, 0.9999999999902659, 0.9999999999902662, 0.9999999999902666, 0.9999999999902662, 0.999999999990266, 0.9999999999902666, 0.9999999999902666, 0.9999999999902659, 0.9999999999902666, 0.999999999990267]\n",
      "Tenperature: 0.391319, FreeEnergy: -2.000000, FreeExact: -2.000000, ExpectX: 1.000000, ExpectXExact: 1.000000\n",
      "ExpectXX:  [0.9999999947089839, 0.999999994708985, 0.9999999947089844, 0.999999994708985, 0.9999999947089856, 0.999999994708985, 0.999999994708984, 0.999999994708985, 0.9999999947089856, 0.9999999947089859, 0.9999999947089853, 0.9999999947089856, 0.999999994708986, 0.9999999947089858, 0.999999994708985]\n",
      "Tenperature: 0.483475, FreeEnergy: -2.000000, FreeExact: -2.000000, ExpectX: 1.000000, ExpectXExact: 1.000000\n",
      "ExpectXX:  [0.9999996091422997, 0.9999996091421799, 0.9999996091422346, 0.999999609142247, 0.999999609142225, 0.999999609142221, 0.9999996091422341, 0.9999996091422534, 0.9999996091422604, 0.9999996091422595, 0.9999996091422546, 0.9999996091422622, 0.9999996091422885, 0.9999996091422793, 0.9999996091422885]\n",
      "Tenperature: 0.575632, FreeEnergy: -2.000001, FreeExact: -2.000001, ExpectX: 0.999998, ExpectXExact: 0.999998\n",
      "ExpectXX:  [0.9999944525112612, 0.9999944524873254, 0.9999944524873196, 0.9999944524873163, 0.9999944524873201, 0.9999944524873186, 0.9999944524873136, 0.9999944524873171, 0.9999944524873122, 0.9999944524873163, 0.9999944524873208, 0.9999944524873201, 0.9999944524873117, 0.9999944524873117, 0.9999944524873103]\n",
      "Tenperature: 0.667789, FreeEnergy: -2.000004, FreeExact: -2.000004, ExpectX: 0.999987, ExpectXExact: 0.999987\n",
      "ExpectXX:  [0.9999620046833689, 0.9999620035605026, 0.9999620035604996, 0.9999620035604988, 0.999962003560501, 0.9999620035604997, 0.9999620035605007, 0.999962003560501, 0.9999620035605014, 0.9999620035604988, 0.9999620035604988, 0.9999620035604984, 0.999962003560498, 0.9999620035604957, 0.9999620035604977]\n",
      "Tenperature: 0.759946, FreeEnergy: -2.000021, FreeExact: -2.000021, ExpectX: 0.999945, ExpectXExact: 0.999945\n",
      "ExpectXX:  [0.9998358203217551, 0.9998357993516206, 0.9998357993513237, 0.9998357993513355, 0.9998357993513357, 0.9998357993513358, 0.9998357993513362, 0.999835799351337, 0.9998357993513365, 0.9998357993513373, 0.999835799351338, 0.9998357993513384, 0.9998357993513399, 0.9998357993513423, 0.9998357993513418]\n",
      "Tenperature: 0.852102, FreeEnergy: -2.000073, FreeExact: -2.000073, ExpectX: 0.999826, ExpectXExact: 0.999826\n",
      "ExpectXX:  [0.999479138753256, 0.9994789275783286, 0.9994789275904118, 0.9994789275892283, 0.9994789275892287, 0.9994789275892286, 0.9994789275892295, 0.9994789275892314, 0.999478927589231, 0.9994789275892313, 0.9994789275892306, 0.9994789275892308, 0.9994789275892317, 0.9994789275892338, 0.9994789275892348]\n",
      "Tenperature: 0.944259, FreeEnergy: -2.000203, FreeExact: -2.000203, ExpectX: 0.999556, ExpectXExact: 0.999556\n",
      "ExpectXX:  [0.998669521034406, 0.9986680439715716, 0.9986680439681883, 0.9986680439693928, 0.9986680439690806, 0.9986680439708547, 0.9986680439696901, 0.9986680439709522, 0.9986680439701648, 0.9986680439698389, 0.998668043968766, 0.9986680439682122, 0.9986680439670101, 0.9986680439665033, 0.9986680439657085]\n",
      "Tenperature: 1.036416, FreeEnergy: -2.000481, FreeExact: -2.000481, ExpectX: 0.999029, ExpectXExact: 0.999029\n",
      "ExpectXX:  [0.9970967717602771, 0.9970897187408994, 0.997089718572463, 0.997089718572327, 0.9970897185725359, 0.9970897185725478, 0.9970897185734028, 0.997089718572975, 0.9970897185730037, 0.9970897185720358, 0.9970897185715073, 0.9970897185712236, 0.9970897185711802, 0.997089718570858, 0.997089718570987]\n",
      "Tenperature: 1.128572, FreeEnergy: -2.001000, FreeExact: -2.001000, ExpectX: 0.998111, ExpectXExact: 0.998111\n",
      "ExpectXX:  [0.9943696597848007, 0.9943430272024375, 0.9943430248053157, 0.9943430248051883, 0.9943430248053611, 0.9943430248051701, 0.9943430248051814, 0.9943430248052532, 0.9943430248052709, 0.994343024805111, 0.994343024805066, 0.9943430248048788, 0.9943430248048795, 0.9943430248044953, 0.994343024804359]\n",
      "Tenperature: 1.220729, FreeEnergy: -2.001884, FreeExact: -2.001884, ExpectX: 0.996636, ExpectXExact: 0.996636\n",
      "ExpectXX:  [0.9900259763645864, 0.9899418917236026, 0.9899418680591761, 0.9899418680559651, 0.9899418680560561, 0.9899418680560184, 0.9899418680560231, 0.9899418680560947, 0.9899418680560669, 0.9899418680560294, 0.9899418680561406, 0.9899418680560961, 0.9899418680561048, 0.9899418680561193, 0.9899418680561325]\n",
      "Tenperature: 1.312886, FreeEnergy: -2.003280, FreeExact: -2.003280, ExpectX: 0.994406, ExpectXExact: 0.994406\n",
      "ExpectXX:  [0.9835424105878935, 0.9833113499380214, 0.9833111703321964, 0.9833111703373154, 0.983311170357641, 0.9833111703704022, 0.9833111703699801, 0.9833111703663886, 0.9833111703674774, 0.9833111703743135, 0.9833111703787991, 0.9833111703561677, 0.9833111703491805, 0.9833111703696609, 0.9833111703582222]\n",
      "Tenperature: 1.405042, FreeEnergy: -2.005365, FreeExact: -2.005365, ExpectX: 0.991180, ExpectXExact: 0.991180\n",
      "ExpectXX:  [0.9743423710522051, 0.9737735802622972, 0.9737724823986714, 0.9737724823851456, 0.9737724823872493, 0.9737724823859325, 0.9737724823792898, 0.9737724823817548, 0.9737724823760479, 0.9737724823731465, 0.9737724823707358, 0.9737724823747363, 0.9737724823803807, 0.973772482381236, 0.9737724823826587]\n",
      "Tenperature: 1.497199, FreeEnergy: -2.008337, FreeExact: -2.008337, ExpectX: 0.986661, ExpectXExact: 0.986661\n",
      "ExpectXX:  [0.9618021030317085, 0.9605198191605273, 0.9605142981216709, 0.9605142978277537, 0.9605142978546111, 0.9605142978429535, 0.9605142978531559, 0.9605142978543743, 0.9605142978502706, 0.9605142978591866, 0.960514297849701, 0.9605142978514366, 0.9605142978548501, 0.9605142978749808, 0.9605142978829205]\n",
      "Tenperature: 1.589356, FreeEnergy: -2.012420, FreeExact: -2.012420, ExpectX: 0.980467, ExpectXExact: 0.980467\n",
      "ExpectXX:  [0.9452544411482109, 0.9425623070064337, 0.942538234491125, 0.9425382296701516, 0.9425382296202489, 0.9425382296885029, 0.942538229720757, 0.9425382296785245, 0.9425382297298712, 0.9425382296680842, 0.942538229791189, 0.9425382297498349, 0.9425382297449185, 0.9425382298735094, 0.9425382299387891]\n",
      "Tenperature: 1.681513, FreeEnergy: -2.017868, FreeExact: -2.017868, ExpectX: 0.972083, ExpectXExact: 0.972083\n",
      "ExpectXX:  [0.9239913208887536, 0.9186592449723474, 0.9185658759437229, 0.9185658057836649, 0.9185658060867252, 0.9185658058682652, 0.9185658060649179, 0.9185658059478315, 0.9185658065692781, 0.9185658064338287, 0.9185658066621606, 0.9185658066694258, 0.9185658067948705, 0.9185658061523532, 0.918565807045874]\n",
      "Tenperature: 1.773669, FreeEnergy: -2.024965, FreeExact: -2.024965, ExpectX: 0.960771, ExpectXExact: 0.960771\n",
      "ExpectXX:  [0.8972653365657299, 0.8872015135447862, 0.8868720187695903, 0.8868711866465495, 0.8868711876498067, 0.8868711868089472, 0.8868711904023038, 0.8868711899877888, 0.8868711897891753, 0.8868711895812016, 0.8868711916805578, 0.8868711908110782, 0.8868711931147717, 0.8868711907073497, 0.8868711958152454]\n",
      "Tenperature: 1.865826, FreeEnergy: -2.034037, FreeExact: -2.034037, ExpectX: 0.945391, ExpectXExact: 0.945391\n",
      "ExpectXX:  [0.8642911295060764, 0.8460475353562635, 0.8449683675520616, 0.8449599559808839, 0.8449599599441601, 0.8449599732805517, 0.8449599665155401, 0.8449599670707155, 0.8449599718576352, 0.8449599877495899, 0.8449599850420615, 0.8449599950839934, 0.8449599758615567, 0.8449599854297765, 0.8449600143484793]\n",
      "Tenperature: 1.957983, FreeEnergy: -2.045467, FreeExact: -2.045467, ExpectX: 0.923993, ExpectXExact: 0.923992\n",
      "ExpectXX:  [0.8242457003567186, 0.7922884038902195, 0.7889560927815197, 0.7888811798846257, 0.7888810515853414, 0.7888810257861463, 0.7888810897246578, 0.7888810675608701, 0.7888810725093859, 0.7888811099979453, 0.7888810818672569, 0.7888811885996745, 0.7888810977535542, 0.7888811141293727, 0.7888812726340013]\n",
      "Tenperature: 2.050139, FreeEnergy: -2.059730, FreeExact: -2.059730, ExpectX: 0.892710, ExpectXExact: 0.892709\n",
      "ExpectXX:  [0.7762834513632312, 0.7219317221929726, 0.7120867787057811, 0.7114691107837535, 0.7114645838597097, 0.7114649580572239, 0.7114648546719844, 0.7114643031092962, 0.7114649890682984, 0.7114646263650406, 0.7114648772830975, 0.7114650527918048, 0.7114647922938621, 0.7114651334053748, 0.7114656489763764]\n",
      "Tenperature: 2.142296, FreeEnergy: -2.077460, FreeExact: -2.077460, ExpectX: 0.841663, ExpectXExact: 0.841661\n",
      "ExpectXX:  [0.7195745108140926, 0.6295594147200175, 0.6014566176303852, 0.5966140098648129, 0.596381926392894, 0.5963769158706764, 0.5963807895173155, 0.5963803000110182, 0.5963810425258613, 0.5963804219016069, 0.5963808041543571, 0.5963819526853547, 0.5963837016920229, 0.5963827251131631, 0.5963847892214414]\n",
      "Tenperature: 2.234453, FreeEnergy: -2.099675, FreeExact: -2.099675, ExpectX: 0.722347, ExpectXExact: 0.722474\n",
      "ExpectXX:  [0.6540236343479173, 0.5089536075930694, 0.43104789388189335, 0.3931471915365483, 0.3800612386960139, 0.37791804387696204, 0.37783665697505747, 0.3778291843500912, 0.3778319659014757, 0.3778519666145601, 0.3778501097778787, 0.3778517504310676, 0.3778521797768001, 0.37785262552361193, 0.3778693500966248]\n",
      "Tenperature: 2.326610, FreeEnergy: -2.128877, FreeExact: -2.128877, ExpectX: 0.000024, ExpectXExact: 0.000000\n",
      "ExpectXX:  [0.5807694755211138, 0.36570065295045084, 0.2097735924785638, 0.09408599100684031, 0.025455043791641003, 0.0025292728526476647, 3.2985238876799285e-05, 1.099023737232252e-06, -1.1020839698841766e-06, 4.852328971192223e-07, -7.196261608833448e-08, -2.755644155722979e-07, 1.2882049854317824e-07, -5.401001121990654e-07, 5.749903921752003e-07]\n",
      "Tenperature: 2.418766, FreeEnergy: -2.164144, FreeExact: -2.164144, ExpectX: 0.000001, ExpectXExact: 0.000000\n",
      "ExpectXX:  [0.5185456122430652, 0.2652299826773097, 0.10175787453944106, 0.020822029016258566, 0.0012027801493853987, 5.529619294996852e-06, -2.3874542085022974e-08, -1.0019334938586121e-07, 1.418311461772701e-08, 8.720121644806781e-08, -1.2849198735296267e-08, 1.3429939245748712e-07, 2.0065378219605113e-09, 2.0968934167993424e-08, -3.115032252818101e-08]\n",
      "Tenperature: 2.510923, FreeEnergy: -2.203203, FreeExact: -2.203203, ExpectX: 0.000001, ExpectXExact: 0.000000\n",
      "ExpectXX:  [0.46639977116408166, 0.19645067092214444, 0.05180793529679292, 0.005083099191102901, 6.84985989640743e-05, 1.6657573437550386e-08, 7.82435346646585e-11, 9.749988390403083e-09, -3.400835376132636e-09, -7.263125658368062e-09, 3.476517305594907e-09, -7.361842188771448e-10, -1.597264032477068e-08, -6.066149905890306e-09, 1.2015367735950024e-08]\n",
      "Tenperature: 2.603080, FreeEnergy: -2.245131, FreeExact: -2.245131, ExpectX: 0.000000, ExpectXExact: 0.000000\n",
      "ExpectXX:  [0.422094556044791, 0.14804737655613795, 0.02741667049642464, 0.0013415580584000186, 4.528043511011872e-06, 6.753854402444039e-11, -1.2324576944810958e-14, -5.324364124501175e-15, -1.8815900033675164e-14, 3.877002112357409e-09, -8.716283174640925e-11, 8.879024119173028e-10, 7.076866256374997e-10, 6.920385675280183e-10, 1.000701392618881e-09]\n",
      "Tenperature: 2.695236, FreeEnergy: -2.289360, FreeExact: -2.289360, ExpectX: 0.000000, ExpectXExact: 0.000000\n",
      "ExpectXX:  [0.3840686257513299, 0.11327574428660715, 0.014998048874063655, 0.0003783634529387564, 3.404855458574699e-07, 3.5579260989774143e-13, -1.8052354543404138e-16, 5.535308346501251e-14, -8.477878703971622e-15, -1.0680443076627792e-14, -3.010474474533579e-13, -7.869443328690174e-14, -4.900150446740784e-10, 6.325439135530055e-10, 1.184367594210152e-10]\n",
      "Tenperature: 2.787393, FreeEnergy: -2.335490, FreeExact: -2.335490, ExpectX: 0.000000, ExpectXExact: 0.000000\n",
      "ExpectXX:  [0.3511686896068362, 0.08784025970711616, 0.00844677209171619, 0.00011315382852083639, 2.8723028926838513e-08, 2.2194870601671342e-15, -1.2035714453774888e-15, -2.3554864961278342e-15, -4.578325978804043e-15, -5.335411678919924e-15, -4.6686895317706035e-14, -3.310963517733496e-14, 6.639716133696719e-14, -3.1168825116747777e-12, 1.055132005619988e-12]\n",
      "Tenperature: 2.879550, FreeEnergy: -2.383222, FreeExact: -2.383222, ExpectX: 0.000000, ExpectXExact: 0.000000\n",
      "ExpectXX:  [0.32249314230157894, 0.06893633439813844, 0.004882332416037341, 3.567011487003848e-05, 2.6901527469955166e-09, 8.082658693508305e-17, -2.8683034498579573e-16, -5.126383153764398e-16, 1.1701522584580845e-15, -9.79995667445024e-15, 6.763197114778394e-16, 4.2498684949311475e-15, 8.830764195649759e-14, -1.0385263550121615e-14, 5.868026410498146e-13]\n",
      "Tenperature: 2.971707, FreeEnergy: -2.432327, FreeExact: -2.432327, ExpectX: 0.000000, ExpectXExact: 0.000000\n",
      "ExpectXX:  [0.29733299007627423, 0.05468751841619401, 0.002888966228725802, 1.179434952185341e-05, 2.772055545219514e-10, -2.77331225917809e-16, 1.4930822011371677e-16, -9.640236720248294e-16, -8.093937639617474e-16, 7.627928896878898e-16, 3.6624766480142045e-15, 6.700259077482599e-12, -1.0899548267715265e-14, -7.574646746340237e-14, 1.373235522111138e-14]\n",
      "Tenperature: 3.063863, FreeEnergy: -2.482619, FreeExact: -2.482619, ExpectX: 0.000000, ExpectXExact: 0.000000\n",
      "ExpectXX:  [0.275123286071317, 0.043810609809417325, 0.0017462582111242245, 4.073402175649063e-06, 3.123172127348991e-11, 3.3943247022408125e-15, -1.6538297378810807e-14, 3.0880883561749904e-14, -2.2020925076534996e-14, 2.2565216662251105e-12, -7.870447235178326e-13, -3.560525246540437e-13, 5.296459411368406e-11, 9.356719129393584e-12, -8.848039037992694e-12]\n",
      "Tenperature: 3.156020, FreeEnergy: -2.533950, FreeExact: -2.533950, ExpectX: 0.000000, ExpectXExact: 0.000000\n",
      "ExpectXX:  [0.25540970898397014, 0.03541218645824972, 0.0010764319966374454, 1.4653305837188648e-06, 3.829995651074678e-12, 6.194725009255564e-15, 4.151183336371076e-15, 4.976696693325775e-15, 3.5110581824562804e-14, 1.0131956039771702e-14, 8.956645943660654e-15, 8.66065943687993e-16, 4.121857918236834e-14, -5.249881564441361e-15, 1.8993520834461418e-16]\n",
      "Tenperature: 3.248177, FreeEnergy: -2.586196, FreeExact: -2.586196, ExpectX: 0.000000, ExpectXExact: 0.000000\n",
      "ExpectXX:  [0.2378232741801551, 0.028858664366725795, 0.0006754403448180653, 5.46645457162365e-07, 5.226343975299561e-13, 7.569272551070673e-15, -3.92442904459128e-16, -1.8290647637926986e-15, -5.841978503261347e-13, -1.5502718919053545e-13, 6.605128329196907e-13, -1.3010077864809313e-12, 3.3438620263678944e-13, -1.9905771037254564e-12, 7.130746393073333e-13]\n",
      "Tenperature: 3.340333, FreeEnergy: -2.639254, FreeExact: -2.639254, ExpectX: 0.000000, ExpectXExact: 0.000000\n",
      "ExpectXX:  [0.22206109952469144, 0.023696267459408588, 0.00043090210053579013, 2.1103864413151427e-07, -2.1984002610644976e-13, 5.323967444440686e-13, 2.48041623546974e-13, 8.718823600788776e-13, -4.611419873071923e-13, 8.135700647152304e-14, 5.87934192868454e-14, -3.16402323444523e-13, 4.722039353522795e-13, 1.420560934550012e-14, -5.67439880589244e-13]\n",
      "Tenperature: 3.432490, FreeEnergy: -2.693035, FreeExact: -2.693035, ExpectX: 0.000000, ExpectXExact: 0.000000\n",
      "ExpectXX:  [0.20787366497800075, 0.019593778835949486, 0.00027921511977997796, 8.410029101576174e-08, 1.923850439520129e-13, 6.750901761093361e-13, 9.345057429321336e-13, 6.934282601955329e-13, 5.263864292401389e-13, 6.959074279689202e-13, -2.9356146549132117e-13, 8.2709658885531e-13, 1.7627430538546906e-13, 2.025930596795049e-13, 1.0901952922277991e-13]\n",
      "Tenperature: 3.524647, FreeEnergy: -2.747467, FreeExact: -2.747467, ExpectX: 0.000000, ExpectXExact: 0.000000\n",
      "ExpectXX:  [0.19505297082729603, 0.01630589780793559, 0.0001833908484108425, 3.444546432616795e-08, -1.2728765569303721e-14, 1.0949724289550864e-13, 2.1683059410567628e-14, -5.382610435645209e-15, -5.3356154830598694e-14, -6.022882706517766e-14, 7.54879140429075e-14, 1.7087732188075734e-13, -8.793095487982116e-14, -5.0915440225818635e-14, -1.1097491486654869e-15]\n",
      "Tenperature: 3.616804, FreeEnergy: -2.802485, FreeExact: -2.802485, ExpectX: 0.000000, ExpectXExact: 0.000000\n",
      "ExpectXX:  [0.18342480957096807, 0.013652011431219893, 0.00012217511907590422, 1.4574062097884231e-08, -2.4873060106150452e-14, 1.1758997912508553e-14, -2.4506945836014345e-14, 1.068990995559906e-13, -9.663532968249699e-14, 1.7226668766977976e-14, -3.843963013327244e-15, -4.53671209579854e-14, 1.0104674922666241e-13, 3.4803972414508375e-14, 1.469236972229613e-14]\n",
      "Tenperature: 3.708960, FreeEnergy: -2.858032, FreeExact: -2.858032, ExpectX: 0.000000, ExpectXExact: 0.000000\n",
      "ExpectXX:  [0.17284226541536224, 0.011494502402286317, 8.239702481896424e-05, 6.3206034727643655e-09, 9.893114578706308e-15, -3.3507454455485003e-14, 1.81461030551799e-15, 2.5027616146934285e-14, 4.85377523667719e-14, 5.3209265709479626e-14, 2.848290049083231e-14, 2.3053759247828736e-14, 3.092436431932232e-14, 3.442126060924973e-14, -1.48609223880975e-14]\n",
      "Tenperature: 3.801117, FreeEnergy: -2.914062, FreeExact: -2.914062, ExpectX: 0.000000, ExpectXExact: 0.000000\n",
      "ExpectXX:  [0.1631807175294912, 0.009728812863364534, 5.6203959015186325e-05, 2.8030139801137433e-09, 2.998946820242627e-14, 3.1519813099325505e-14, 1.987779320855071e-14, 1.5243341007218424e-15, 1.3248317572937185e-14, -1.074949249315412e-15, 2.0707021321064505e-14, 1.0683215549898974e-14, 6.230298716479492e-14, 1.5166769369999801e-13, 2.7548432854206477e-15]\n",
      "Tenperature: 3.893274, FreeEnergy: -2.970530, FreeExact: -2.970530, ExpectX: 0.000000, ExpectXExact: 0.000000\n",
      "ExpectXX:  [0.1543337486237418, 0.008275061523607387, 3.8776790694760354e-05, 1.2768173495439207e-09, 1.2610645656359673e-13, 1.557337325668964e-14, 3.218636941120482e-14, 1.4786302160125887e-13, 4.667751061018266e-14, 5.638092690397707e-14, 4.8785571167653114e-14, 4.2929694385038595e-14, 8.272698653544656e-14, 6.4187596600007505e-15, 3.4792936414676944e-14]\n",
      "Tenperature: 3.985430, FreeEnergy: -3.027400, FreeExact: -3.027400, ExpectX: 0.000000, ExpectXExact: 0.000000\n",
      "ExpectXX:  [0.14621032729794542, 0.007071037381960844, 2.701101194951077e-05, 5.894816625355459e-10, 3.7637171745531494e-13, 6.702650909934094e-13, 7.043417136736749e-13, 1.3766458053829328e-15, 1.1391647812347453e-13, 2.028582530956427e-15, 2.8375726385620904e-13, 3.844225777794463e-13, 1.7523004207310704e-13, 2.6982689276572728e-14, 6.188411489575364e-15]\n",
      "Tenperature: 4.077587, FreeEnergy: -3.084639, FreeExact: -3.084639, ExpectX: 0.000000, ExpectXExact: 0.000000\n",
      "ExpectXX:  [0.13873177222963043, 0.006068827053734652, 1.901910742294252e-05, 2.8029771642711223e-10, 1.2249948285270286e-14, 3.2488591137166816e-14, 3.568490005154365e-15, 4.3058899160438314e-14, 6.023150423188078e-14, 2.683569079525913e-14, 3.538675642633148e-14, 4.56631648895383e-15, 1.1499589722113484e-14, 8.38558524882159e-15, 1.1180678349473327e-14]\n",
      "Tenperature: 4.169744, FreeEnergy: -3.142217, FreeExact: -3.142217, ExpectX: 0.000000, ExpectXExact: 0.000000\n",
      "ExpectXX:  [0.13183013039455704, 0.005229980219146251, 1.35115049180076e-05, 1.3560837728249908e-10, 5.075555714796688e-16, 2.3338733849179535e-14, 3.1897310490266116e-14, 3.041739206557718e-15, 3.87603836526037e-15, 7.435463713838948e-15, 8.972452145040632e-15, 1.7222163046154213e-14, -2.9598126546826265e-17, 3.3069426504650232e-15, 3.4448597156962606e-15]\n",
      "Tenperature: 4.261900, FreeEnergy: -3.200108, FreeExact: -3.200108, ExpectX: 0.000000, ExpectXExact: 0.000000\n",
      "ExpectXX:  [0.12544604196985035, 0.004524859298312673, 9.681816542969662e-06, 6.665514166271716e-11, 2.3139553986817275e-16, 4.583518785636857e-15, 7.459878069632109e-15, 2.9335128127143616e-15, 3.674999902763672e-15, 1.4380338368799633e-14, 6.568540131399558e-16, 1.6344593392661473e-14, -3.7721519241906935e-17, 7.294334699127375e-15, 1.069835476793956e-15]\n",
      "Tenperature: 4.354057, FreeEnergy: -3.258289, FreeExact: -3.258289, ExpectX: 0.000000, ExpectXExact: 0.000000\n",
      "ExpectXX:  [0.11952817194185679, 0.003928943261920109, 6.994208514865224e-06, 3.331781524547937e-11, 9.254367305262263e-15, 7.546196886550521e-18, 2.0100247426379424e-15, 2.3081041982095378e-14, 3.248218021556852e-15, 2.8864884146771752e-15, 4.397790400193231e-15, 5.271896468875019e-15, 3.690601507837108e-15, 7.784210852269773e-16, 4.792405088986584e-16]\n",
      "Tenperature: 4.446214, FreeEnergy: -3.316737, FreeExact: -3.316737, ExpectX: 0.000000, ExpectXExact: 0.000000\n",
      "ExpectXX:  [0.11403104025059689, 0.0034236215279917436, 5.093801718741057e-06, 1.7052446739127784e-11, 7.225459746461682e-15, 5.877406845627944e-15, 8.717415217565715e-15, 1.957211462661664e-15, 1.4187570592316802e-14, 1.118245464670043e-14, 4.196716768849258e-14, 3.723424699751838e-15, 2.901589187489115e-15, 4.4252188384232895e-15, 2.401271243475085e-15]\n",
      "Tenperature: 4.538371, FreeEnergy: -3.375435, FreeExact: -3.375435, ExpectX: 0.000000, ExpectXExact: 0.000000\n",
      "ExpectXX:  [0.10891523278403696, 0.0029926353496876517, 3.7366644613587764e-06, 8.821912689158627e-12, 5.314802027462196e-14, 2.5598188158169677e-15, 3.4518190503765986e-14, 1.897628158538253e-15, 5.3192035928425215e-14, 2.355402431687197e-15, 1.5871443242504184e-14, 2.9237392243156103e-16, 8.659516267073705e-15, 1.7981915352235818e-14, 1.9562352987023763e-15]\n"
     ]
    }
   ],
   "source": [
    "##### Example 1: square lattice classical Ising model #####\n",
    "###########################################################\n",
    "\n",
    "N = 50\n",
    "numlevels = 16 # number of coarse-grainings\n",
    "Tc = (2/np.log(1+np.sqrt(2)))\n",
    "relTemp = np.linspace(0.01, 2.0, N)\n",
    "T = relTemp*Tc\n",
    "\n",
    "FreeEnergy = [0 for x in range(N)]\n",
    "FreeExact = [0 for x in range(N)]\n",
    "ExpectX = [0 for x in range(N)]\n",
    "ExpectXExact = [0 for x in range(N)]\n",
    "ExpectXX = [0 for x in range(N)]\n",
    "\n",
    "for i in range(N):\n",
    "    Tval  = T[i]\n",
    "    #----------------------------------------------------\n",
    "    # Evaluate obserables of interest\n",
    "    A, vC, wC, Anorm = iterTRG(numlevels, Tval)\n",
    "    FreeEnergy[i], FreeExact[i], ExpectX[i], ExpectXExact[i], ExpectXX[i] = evalTRG(numlevels, Tval, A, vC, wC, Anorm)\n",
    "    print('Tenperature: %f, FreeEnergy: %f, FreeExact: %f, ExpectX: %f, ExpectXExact: %f' % (Tval, FreeEnergy[i], FreeExact[i], ExpectX[i], ExpectXExact[i]))\n",
    "    print('ExpectXX: ', ExpectXX[i])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 绘制曲线\n",
    "plt.plot(T, ExpectXExact)\n",
    "plt.scatter(T, ExpectX)\n",
    "\n",
    "plt.tick_params(direction='in') \n",
    "\n",
    "# 添加网格线\n",
    "plt.grid(True)\n",
    "\n",
    "# 添加标签和标题\n",
    "plt.xlabel('Temperature')\n",
    "plt.ylabel('Magnetization')\n",
    "plt.title('T-M curve')\n",
    "\n",
    "# 显示图形\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 绘制曲线\n",
    "plt.plot(T, FreeExact, color='r')\n",
    "plt.scatter(T, FreeEnergy, color='r')\n",
    "\n",
    "plt.tick_params(direction='in') \n",
    "\n",
    "# 添加网格线\n",
    "plt.grid(True)\n",
    "\n",
    "# 添加标签和标题\n",
    "plt.xlabel('Temperature')\n",
    "plt.ylabel('Free Energy')\n",
    "plt.title('T-F curve')\n",
    "\n",
    "# 显示图形\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "data = np.array(ExpectXX).transpose()\n",
    "\n",
    "plt.imshow(data, cmap='viridis_r', extent=[0, T[N-1], 15, 0], aspect=0.3)  # 设置颜色映射和范围\n",
    "plt.colorbar()\n",
    "\n",
    "# 添加标签和标题\n",
    "plt.xlabel('Temperature')\n",
    "plt.ylabel('log_2(Distance)')\n",
    "plt.title('Two Spins Correlation')\n",
    "\n",
    "# 显示图形\n",
    "plt.show()"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "autodiff",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.12.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}