Factorized finite-size Ising model spin matrix elements from Separation of Variables

TL;DR

This paper derives factorized formulas for finite-size Ising model spin matrix elements using the Separation of Variables method, confirming a recent conjecture and advancing exact solutions in statistical mechanics.

Contribution

It introduces a novel application of the Separation of Variables method to derive explicit factorized formulas for Ising model spin matrix elements, validating a recent conjecture.

Findings

Derived explicit factorized formulas for spin matrix elements

Confirmed the conjecture by Bugrij and Lisovyy

Enhanced understanding of finite-size Ising models

Abstract

Using the Sklyanin-Kharchev-Lebedev method of Separation of Variables adapted to the cyclic Baxter--Bazhanov--Stroganov or $\tau^{(2)}$-model, we derive factorized formulae for general finite-size Ising model spin matrix elements, proving a recent conjecture by Bugrij and Lisovyy.