Ising Matter as Bulky: An Identity Described by Many Models

TL;DR

This paper explores the multifaceted nature of the 2D Ising model, revealing surprising features and analogies with mathematical structures, highlighting its rich theoretical landscape.

Contribution

It introduces new perspectives on the Ising model by connecting its properties to classical mathematical analogies, offering deeper theoretical insights.

Findings

Multiple computational approaches reveal different features of Ising Matter.

Analogies with analysis, algebra, and arithmetic deepen understanding of the model.

Surprising properties emerge from various methods of studying the Ising model.

Abstract

The two-dimensional Ising model of a ferromagnet allows for many ways of computing its partition function and other properties. Each way reveals surprising features of what we might call Ising Matter. Moreover, the various ways would appear to analogize with the mathematical threefold analogy of analysis, algebra, and arithmetic, due to R. Dedekind and H. Weber, 1882, and more recently described by A. Weil.