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View Code? Open in Web Editor NEWLattice 2d phi^4 calculations accelerated by cluster updates of the embedded Ising variables
License: GNU General Public License v3.0
Lattice 2d phi^4 calculations accelerated by cluster updates of the embedded Ising variables
License: GNU General Public License v3.0
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
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