Probability distribution of the order parameter for the 3D Ising model universality class: a high precision Monte Carlo study

TL;DR

This study uses high-precision Monte Carlo simulations to analyze the probability distribution of the order parameter in the 3D Ising universality class, providing new insights into its universal shape at criticality.

Contribution

The paper presents the most precise determination of the order parameter distribution for the 3D Ising model and its generalization, along with an accurate universal approximation formula.

Findings

High-precision P(M) distribution obtained at criticality

Universal shape of P(M) accurately described by a simple formula

Reduced corrections to scaling enable unprecedented accuracy

Abstract

We study the probability distribution P(M) of the order parameter (average magnetization) M, for the finite-size systems at the critical point. The systems under consideration are the 3-dimensional Ising model on a simple cubic lattice, and its 3-state generalization known to have remarkably small corrections to scaling. Both models are studied in a cubic box with periodic boundary conditions. The model with reduced corrections to scaling makes it possible to determine P(M) with unprecedented precision. We also obtain a simple, but remarkably accurate approximate formula describing the universal shape of P(M).