Complete high-precision entropic sampling

TL;DR

This paper introduces tomographic entropic sampling, a novel Monte Carlo method that accurately estimates the number of configurations across the full energy range without dividing into subsets, demonstrated on Ising and lattice gas models.

Contribution

The paper presents a new entropic sampling scheme that improves precision and efficiency by using multiple studies from different regions, avoiding energy window division.

Findings

Achieved critical temperature accuracy of 0.01% for the 2D Ising model.

Estimated critical exponents within 1% of known values.

Results for 3D Ising and lattice gas models closely match literature and exact results.

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.