Some comments on developments in exact solutions in statistical mechanics since 1944

TL;DR

This paper reviews developments in exact solutions of statistical mechanics models since 1944, highlighting how recent work revisits properties initially observed by Onsager and Kaufman in the Ising model.

Contribution

It provides a historical overview and discusses recent trends in exact solutions, emphasizing the resurgence of properties found in early foundational work.

Findings

Recent work revisits Onsager and Kaufman's properties

Advances in solving more complex models

Historical perspective on exact solutions

Abstract

Lars Onsager and Bruria Kaufman calculated the partition function of the Ising model exactly in 1944 and 1949. Since then there have been many developments in the exact solution of similar, but usually more complicated, models. Here I shall mention a few, and show how some of the latest work seems to be returning once again to the properties observed by Onsager and Kaufman.