On the diagonal susceptibility of the 2D Ising model

TL;DR

This paper investigates the diagonal susceptibility of the 2D Ising model below the critical temperature, proving that the unit circle forms a natural boundary for the extended susceptibility function.

Contribution

It extends the diagonal susceptibility to complex parameters and proves the conjecture that the unit circle is a natural boundary, a significant insight into the model's analytic structure.

Findings

Extended susceptibility to complex parameters inside the unit disc

Proved the unit circle as a natural boundary for the susceptibility

Confirmed conjecture about the analytic properties of the 2D Ising model

Abstract

We consider the diagonal susceptibility of the isotropic 2D Ising model for temperatures below the critical temperature. For a parameter k related to temperature and the interaction constant, we extend the diagonal susceptibility to complex k inside the unit disc, and prove the conjecture that the unit circle is a natural boundary.