The susceptibility of the two-dimensional Ising model

Abstract

While the free energy and spontaneous magnetisation of the two-dimensional Ising model have been known for more than 60 years, the susceptibility is still not completely known. Some 10 years ago we discovered and implemented a polynomial time algorithm for the series expansion of the susceptibility for the square lattice Ising model. This has recently been improved and applied to other lattices, such as the triangular, honeycomb and kagome lattices. An enormous amount of numerical data has been obtained and analysed, allowing a number of fundamental constants in the problem to be obtained to previously unimaginable precision. It remains an open problem to identify these constants, though we believe that they are related to solutions of the Painlev\'e equations. This project has been conducted, over the years, with Yao-ban Chan, Iwan Jensen, Bernie Nickel, Will Orrick and Jacques Perk.

Details