Form factor representation of the correlation function of the two dimensional Ising model on a cylinder

TL;DR

This paper derives the correlation function for the 2D Ising model on a finite cylinder, providing form factor expansions for different phases and analyzing finite size effects and scaling limits.

Contribution

It introduces a form factor representation of the correlation function for the finite 2D Ising model, including finite size effects and scaling behavior.

Findings

Derived correlation functions for finite lattice with periodic boundary conditions

Obtained form factor expansions for paramagnetic and ferromagnetic phases

Analyzed finite size effects and scaling limits

Abstract

The correlation function of the two dimensional Ising model with the nearest neighbours interaction on the finite size lattice with the periodical boundary conditions is derived. The expressions similar to the form factor expansion are obtained both for the paramagnetic and ferromagnetic regions of coupling parameter. The peculiarities caused by finite size are analyzed. The scaling limit of the lattice form factor expansion is evaluated.