A unified treatment of Ising model magnetizations

TL;DR

This paper presents a unified analytical approach to compute bulk, surface, and corner magnetizations in the square lattice Ising model, deriving exact expressions for anisotropic cases using functional equations from corner transfer matrices.

Contribution

It introduces a novel method based on functional equations from corner transfer matrices to unify the calculation of various magnetizations in the Ising model.

Findings

Derived exact formulas for magnetizations with anisotropy

Verified known results and obtained new analytical expressions

Extended understanding of corner effects in the Ising model

Abstract

We show how the spontaneous bulk, surface and corner magnetizations in the square lattice Ising model can all be obtained within one approach. The method is based on functional equations which follow from the properties of corner transfer matrices and vertex operators and which can be derived graphically. In all cases, exact analytical expressions for general anisotropy are obtained. Known results, including several for which only numerical computation was previously possible, are verified and new results related to general anisotropy and corner angles are obtained.