Probability distribution of the order parameter

TL;DR

This paper presents a Monte Carlo simulation method to accurately determine the probability distribution of the order parameter in magnetic systems, aiding in identifying critical points even when the transition temperature is unknown.

Contribution

A novel approach combining Monte Carlo simulations, finite-size scaling, and histogram reweighting to determine the order parameter distribution without prior knowledge of the transition temperature.

Findings

Method accurately identifies criticality in Ising models

Effective even when the transition temperature is unknown

Demonstrated on 2D spin-1/2 and spin-1 Ising models

Abstract

The probability distribution of the order parameter is exploited in order to obtain the criticality of magnetic systems. Monte Carlo simulations have been employed by using single spin flip Metropolis algorithm aided by finite-size scaling and histogram reweighting techniques. A method is proposed to obtain this probability distribution even when the transition temperature of the model is unknown. A test is performed on the two-dimensional spin-1/2 and spin-1 Ising model and the results show that the present procedure can be quite efficient and accurate to describe the criticality of the system.