CONTENTS
--Compilation and dependencies
--Usage and input
--Output
--A brief sketch of the phase diagram
--Comparison with arXiv:0902.0045


+++COMPILATION AND DEPENDENCIES
To compile the (serial) executable `2d_phi4` using g++, just run `make`
GSL is required: https://www.gnu.org/software/gsl/


+++USAGE AND INPUT
The `2d_phi4` program takes five command-line parameters:
  $ ./2d_phi4  mu_0^2  lambda  L  init  meas

* mu_0^2 is the bare mass squared in the lagrangian
* lambda is the bare phi^4 coupling in the lagrangian
* L is the length of each side of the (square) lattice
* init is the number of iterations with which to initialize the system
* meas is the number of iterations subsequently run with measurements

Lagrangian normalization conventions (in euclidean space):
  L = (1/2)d_nu phi d^nu phi + (1/2)mu_0^2 phi^2 + (1/4)lambda phi^4


+++OUTPUT
Each iteration consists of _gap_ Metropolis sweeps of the lattice,
followed by a Wolff cluster flip acting on the embedded Ising system
Currently gap=5 is hard-coded, but may not be optimal...

After each Metropolis + Wolff iteration we print:
* The energy E and magnetization phi
* The position-space two-point function (L/2 real components)
* The momentum-space two-point function (L/2 complex components)

The spatial two-point function uses simple "Manhattan distances"
This can be improved if it would be worthwhile...

At the end of the _meas_ iterations we print:
* The autocorrelation time of |phi|,
  the resulting (non-integer) number of decorrelated measurements
  and the normalization Chi[0] of the autocorrelation function
* The average energy <E> and <|phi|>
  with uncertainties incorporating the autocorrelation time,
  and <phi> itself
  (which should be near zero due to either disorder or cluster flipping)
* Derived quantities:
  The specific heat <E^2> - <E>^2
  The susceptibility <phi^2> - <|phi|>^2
  The Binder cumulant 1 - <phi^4> / (3 * <phi^2>^2);
  The bimodality (with a 21-bin histogram currently hard-coded)
* The average position-space two-point function (without uncertainties)
* The average momentum-space two-point function (without uncertainties)

Currently no uncertainties are estimated for the derived quantities
If we continue to include them
(rather than moving these analyses to offline scripts)
then a jackknife or bootstrap procedure should be added...


+++A BRIEF SKETCH OF THE PHASE DIAGRAM
We typically fix lambda and vary mu_0 to find the transition
Listed below are the approximate mu_0 of the transition for various lambda
The transitions are broader for smaller L and sharpen as L increases
Less negative mu_0 put the system in the symmetric (disordered) phase
More negative mu_0 put the system in the broken (ordered) phase
  lambda = 1.00 --> mu_0 ~ -1.27
  lambda = 0.70 --> mu_0 ~ -0.95
  lambda = 0.50 --> mu_0 ~ -0.72
  lambda = 0.25 --> mu_0 ~ -0.40
  lambda = 0.10 --> mu_0 ~ -0.18
  lambda = 0.05 --> mu_0 ~ -0.10
  lambda = 0.03 --> mu_0 ~ -0.06
  lambda = 0.02 --> mu_0 ~ -0.04
  lambda = 0.01 --> mu_0 ~ -0.02


+++COMPARISON WITH arXiv:0902.0045
These are some 32x32 lambda=0.5 results included in arXiv:0902.0045
$ cd ~/zarchives/Amherst/thesis/code/Phi4/productionRun/
$ grep "^-0.7,0.5" 32-50.csv

arXiv:0902.0045 says that file used 16384+16384 iterations, so compare it with
$ time ./2d_phi4 -0.7 0.5 32 16384 16384

Comparison:   arXiv     current
  <E>         0.359025  0.359657
  <E>_err     0.000979  0.000906
  <|phi|>     0.434639  0.432487
  <|phi|>_err 0.006402  0.005864
  spec heat   0.806815  0.798230
  suscept    34.468476 33.440455
  binder      0.524037  0.526073
  bimod       0.707902  0.751980
  <phi>       0.001692  0.006261
  autocor     9.974279  8.625745
  autocor(0)  0.033661  0.032657