Magnetic susceptibility of the 2D Ising model on a finite lattice

TL;DR

This paper generalizes the form factor approach to compute the magnetic susceptibility of the 2D Ising model on finite lattices, analyzing its singularity structure in both finite and infinite size limits.

Contribution

It extends the form factor representation to arbitrary spin configurations and calculates susceptibility for finite lattice widths, exploring singularities in the complex temperature plane.

Findings

Susceptibility computed for finite lattice widths in both paramagnetic and ferromagnetic phases.

Analysis of the singularity structure of susceptibility in the complex temperature plane.

Comparison of finite-size susceptibility behavior with the thermodynamic limit.

Abstract

Form factor representation of the correlation function of the 2D Ising model on a cylinder is generalized to the case of arbitrary disposition of correlating spins. The magnetic susceptibility on a lattice, one of whose dimensions ($N$) is finite, is calculated in both para- and ferromagnetic regions of parameters of the model. The singularity structure of the susceptibility in the complex temperature plane at finite values of $N$ and the thermodynamic limit $N\to\infty$ are discussed.