Probability Distribution Function of the Order Parameter: Mixing Fields and Universality

TL;DR

This paper reviews how the probability distribution function of the order parameter, especially with mixing fields, can be used to determine critical properties in various statistical models through Monte Carlo simulations.

Contribution

It highlights the role of mixing fields in asymmetric models and discusses the distribution of conjugate variables, providing insights into universality and critical behavior.

Findings

Demonstrates the use of order parameter distributions in critical property analysis

Emphasizes the importance of mixing fields in asymmetric models

Provides examples with various lattice spin systems

Abstract

We briefly review the use of the order parameter probability distribution function as a useful tool to obtain the critical properties of statistical mechanical models using computer Monte Carlo simulations. Some simple discrete spin magnetic systems on a lattice, such as Ising, general spin-$S$ Blume-Capel and Baxter-Wu, $Q$-state Potts, among other models, will be considered as examples. The importance and the necessity of the role of mixing fields in asymmetric magnetic models will be discussed in more detail, as well as the corresponding distributions of the extensive conjugate variables.