Accurate Estimates of 3D Ising Critical Exponents Using the Coherent-Anomaly Method

TL;DR

This paper improves the coherent-anomaly method to estimate 3D Ising model critical exponents accurately, achieving results comparable to the best conventional methods through enhanced data analysis schemes.

Contribution

It introduces an improved CAM data analysis scheme and demonstrates its effectiveness in accurately estimating 3D Ising critical exponents.

Findings

Critical exponents: α=0.11, β=0.33, γ=1.24, δ=4.8

Enhanced CAM scheme reduces errors in critical exponent estimation

Results are comparable to the most precise conventional methods

Abstract

An analysis of the critical behavior of the three-dimensional Ising model using the coherent-anomaly method (CAM) is presented. Various sources of errors in CAM estimates of critical exponents are discussed, and an improved scheme for the CAM data analysis is tested. Using a set of mean-field type approximations based on the variational series expansion approach, accuracy comparable to the most precise conventional methods has been achieved. Our results for the critical exponents are given by $\alpha=\afin$, $\beta=\bfin$, $\gamma=\gfin$ and $\delta=\dfin$.