An Extension of Phenomenological Renormalization Method

TL;DR

This paper introduces an improved cumulant crossing method for more accurate determination of critical points in Monte Carlo simulations, demonstrated on the 2D Ising model.

Contribution

It extends the cumulant crossing method by combining multiple order-parameter moments to reduce systematic errors.

Findings

Method effectively reduces deviation of crossing points from true critical point.

Performance validated on the 2D Ising model.

Provides more precise critical point estimation.

Abstract

We present an extension of the so-called cumulant crossing method which is used for determination of critical point in Monte Carlo simulations.The new method uses linear combination of several different order-parameter moments and almost eliminates the systematic deviation of crossing points from the true critical point. The performance of the method is tested by applying it to the 2D Ising model.