Critical point determination from probability distribution functions in the three dimensional Ising model

TL;DR

This paper introduces a novel numerical method to accurately determine critical points and exponents in the 3D Ising model by analyzing derivatives of the probability distribution function, avoiding correction-to-scaling issues.

Contribution

The authors develop a new algorithm that directly evaluates derivatives of the log probability distribution, providing improved accuracy in critical parameter estimation for the 3D Ising model.

Findings

Method yields results consistent with previous studies.

Correction-to-scaling effects are absent in this approach.

Accurate determination of critical exponents achieved.

Abstract

In this work we propose a new numerical method to evaluate the critical point, the susceptibility critical exponent and the correlation length critical exponent of the three dimensional Ising model without external field using an algorithm that evaluates directly the derivative of the logarithm of the probability distribution function with respect to the magnetisation. Using standard finite-size scaling theory we found that correction-to-scaling effects are not present within this approach. Our results are in good agreement with previous reported values for the three dimensional Ising model.