Three-dimensional Ising models -- Critical Parameters using $\epsilon$-convergence method

TL;DR

This paper applies the $psilon$-convergence method to accurately determine critical temperatures and exponents in three-dimensional Ising models across various lattice types, enhancing precision in critical parameter estimation.

Contribution

It demonstrates the effectiveness of the $psilon$-convergence algorithm in analyzing critical parameters for 3D Ising models on multiple lattice structures, including modifications for improved accuracy.

Findings

Accurate critical temperatures obtained for different lattices.

Effective use of two inverse temperature variables for estimation.

Validation of the $psilon$-convergence method's applicability.

Abstract

We demonstrate the applicability of the $\epsilon$-convergence algorithm in extracting the critical temperatures and critical exponents of three-dimensional Ising models. We analyze the low temperature magnetization as well as high temperature susceptibility series of simple cubic, body-centered cubic, face-centered cubic and diamond lattices, using two different variables for the inverse critical temperature. In the case of simple cubic lattices, the magnetization series was modified to deduce accurate values of the critical temperatures. The alternate variable for dimensionless inverse temperature suggested by Guttmann and Thompson has also been employed for the estimation of the critical parameters.