Analytic average magnetization expression for the body centered cubic Ising lattice

TL;DR

This paper derives an analytic expression for the average magnetization of the body-centered cubic Ising lattice, extending previous studies to a more complex lattice structure and validating it with numerical data.

Contribution

It introduces a new analytic magnetization expression for the body-centered cubic Ising model based on recent interrelation techniques and conjectures for odd spin correlations.

Findings

Analytic magnetization expression matches numerical data well.

Extends previous lattice studies to body-centered cubic structure.

Provides insights into odd spin correlation functions.

Abstract

Recently we have performed large-scale average magnetization studies of the Ising model for the square, honeycomb, triangular, and simple cubic lattice. We want to complement those studies with the structurally more complicated body-centered cubic lattice Ising model in this paper. We have relevantly calculated the order parameter or average magnetization expression for the body-centered cubic Ising lattice based on the recently developed interrelation, given by $\langle\sigma_{0, i}\rangle= \langle\tanh[K(\sigma_{1,i}+\sigma_{2,i}+\dots +\sigma_{z,i})+H]\rangle$. We will use the same conjectures for the odd spins correlation functions as in our previous works. The mathematical forms of the odd spin correlation functions will be eventually elucidated by some physical discussions. We have seen that the obtained average magnetization expression with the numerical data for the body-centered cubic lattice Ising model is in good agreement.