Form-factors in the Baxter-Bazhanov-Stroganov model II: Ising model on the finite lattice

TL;DR

This paper derives a new factorized formula for form-factors of the finite lattice Ising model using separation of variables, providing explicit matrix elements of the spin operator in a transverse field.

Contribution

It presents the first derivation of the factorized form-factors for the finite lattice Ising model, confirming previous conjectures and extending the understanding of the model's matrix elements.

Findings

Derived the factorized formula for Ising model form-factors on finite lattices.

Calculated matrix elements of the spin operator in the finite quantum Ising chain.

Confirmed previous conjectures regarding form-factor structures.

Abstract

We continue our investigation of the Baxter-Bazhanov-Stroganov or \tau^{(2)}-model using the method of separation of variables [nlin/0603028,arXiv:0708.4342]. In this paper we derive for the first time the factorized formula for form-factors of the Ising model on a finite lattice conjectured previously by A.Bugrij and O.Lisovyy in [arXiv:0708.3625,arXiv:0708.3643]. We also find the matrix elements of the spin operator for the finite quantum Ising chain in a transverse field.