Domain magnetization approach to the isothermal critical exponent

TL;DR

This paper introduces a novel method for accurately calculating the isothermal critical exponent in Ising models by analyzing magnetization time series within small lattice domains, especially effective near the pseudocritical point.

Contribution

The paper presents a new approach based on magnetization time series analysis to determine the critical exponent, overcoming limitations of traditional methods.

Findings

Accurately calculates the critical exponent δ for the square-lattice Ising model.

Demonstrates the method's effectiveness where traditional approaches fail.

Provides a simple analytical relation between power-law exponent and δ.

Abstract

We propose a method for calculating the isothermal critical exponent $\delta$ in Ising systems undergoing a second-order phase transition. It is based on the calculation of the mean magnetization time series within a small connected domain of a lattice after equilibrium is reached. At the pseudocritical point, the magnetization time series attains intermittent characteristics and the probability density for consecutive values of mean magnetization within a region around zero becomes a power law. Typically the size of this region is of the order of the standard deviation of the magnetization. The emerging power-law exponent is directly related to the isothermal critical exponent $\delta$ through a simple analytical expression. We employ this method to calculate with remarkable accuracy the exponent $\delta$ for the square-lattice Ising model where traditional approaches, like the constrained effective potential, typically fail to provide accurate results.