Universal features and tail analysis of the order-parameter distribution of the two-dimensional Ising model: An entropic sampling Monte Carlo study

TL;DR

This study uses advanced entropic sampling Monte Carlo methods to analyze the universal features and tail behavior of the order-parameter distribution in the 2D Ising model, providing insights into universal constants and the equation of state.

Contribution

It introduces a combined Wang-Landau and broad histogram entropic sampling approach to accurately study the universal PDF and tail behavior of the 2D Ising model.

Findings

Identification of a stable window for the scaled order-parameter

Estimation of the equation of state exponent

Determination of the Privman-Fisher universal coefficient

Abstract

We present a numerical study of the order-parameter probability density function (PDF) of the square Ising model for lattices with linear sizes $L=80-140$. A recent efficient entropic sampling scheme, combining the Wang-Landau and broad histogram methods and based on the high-levels of the Wang-Landau process in dominant energy subspaces is employed. We find that for large lattices there exists a stable window of the scaled order-parameter in which the full ansatz including the pre-exponential factor for the tail regime of the universal PDF is well obeyed. This window is used to estimate the equation of state exponent and to observe the behavior of the universal constants implicit in the functional form of the universal PDF. The probability densities are used to estimate the universal Privman-Fisher coefficient and to investigate whether one could obtain reliable estimates of the universal constants controlling the asymptotic behavior of the tail regime.