The saga of the Ising susceptibility

TL;DR

This paper reviews the historical progress and mathematical expressions related to the Ising model's susceptibility, focusing on form factors, theta functions, and generalized correlations, highlighting key developments since 1959.

Contribution

It provides a comprehensive review of analytical expressions and developments in the Ising susceptibility, including explicit computations of generalized correlations using theta functions.

Findings

Comparison of form factor expressions in terms of nome and modulus

Explicit computation of generalized correlations for specific cases

Insight into the mathematical structure of Ising susceptibility

Abstract

We review developments made since 1959 in the search for a closed form for the susceptibility of the Ising model. The expressions for the form factors in terms of the nome $q$ and the modulus $k$ are compared and contrasted. The $\lambda$ generalized correlations $C(M,N;\lambda)$ are defined and explicitly computed in terms of theta functions for $M=N=0,1$.