Complete high-precision entropic sampling

Abstract

Monte Carlo simulations using entropic sampling to estimate the number of configurations of a given energy are a valuable alternative to traditional methods. We introduce {\it tomographic} entropic sampling, a scheme which uses multiple studies, starting from different regions of configuration space, to yield precise estimates of the number of configurations over the {\it full range} of energies, {\it without} dividing the latter into subsets or windows. Applied to the Ising model on the square lattice, the method yields the critical temperature to an accuracy of about 0.01%, and critical exponents to 1% or better. Predictions for systems sizes L=10 - 160, for the temperature of the specific heat maximum, and of the specific heat at the critical temperature, are in very close agreement with exact results. For the Ising model on the simple cubic lattice the critical temperature is given to within 0.003% of the best available estimate; the exponent ratios $\beta /\nu$ and $\gamma /\nu$ are given to within about 0.4% and 1%, respectively, of the literature values. In both two and three dimensions, results for the {\it antiferromagnetic} critical point are fully consistent with those of the ferromagnetic transition. Application to the lattice gas with nearest-neighbor exclusion on the square lattice again yields the critical chemical potential and exponent ratios $\beta /\nu$ and $\gamma /\nu$ to good precision.

For a version with figures go to http://www.fisica.ufmg.br/~dickman/transfers/preprints/entsamp2.pdf

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• Macroscopically constrained Wang-Landau method for systems with multiple order parameters and its application to drawing complex phase diagrams
• Convex Hulls of Random Walks in Higher Dimensions: A Large Deviation Study
• On the non-convergence of the Wang-Landau algorithms with multiple random walkers
• Intrinsic convergence properties of entropic sampling algorithms
• Perturbation method to calculate the density of states
• Dynamically Optimized Wang-Landau Sampling with Adaptive Trial Moves and Modification Factors
• Large deviations of connected components in the stochastic block model
• Rejection-free cluster Wang-Landau algorithm for hard-core lattice gases