Legerdemain in Mathematical Physics: Structure, Tricks, and Lacunae in Derivations of the Partition Function of the Two-Dimensional Ising Model and in Proofs of The Stability of Matter

TL;DR

This paper reviews derivations of the partition function of the 2D Ising Model and proofs of matter stability, highlighting gaps and complexities that can mystify readers and suggesting the need for clearer expositions.

Contribution

It provides a critical analysis of existing derivations and proofs, emphasizing the importance of clarity and the identification of lacunae in mathematical physics literature.

Findings

Identification of common gaps in derivations

Insights into the physics behind technical steps

Recommendations for clearer pedagogical explanations

Abstract

We review various derivations of the partition function of the two-dimensional Ising Model of ferromagnetism and proofs of the stability of matter, paying attention to passages where there would appear to be a lacuna between steps or where the structure of the argument is not so straightforward. Authors cannot include all the intermediate steps, but sometimes most readers and especially students will be mystified by such a transition. Moreover, careful consideration of such lacunae points to interesting physics and not only mathematical technology. Also, when reading the original papers, the structure of the physics argument may be buried by the technical moves. Improvements in the derivations, in subsequent papers by others, may well be clearer and more motivated. But, there is remarkably little written and published about how to read some of the original papers, and the subsequent ones, yet students and their teachers would often benefit from such guidance. I should note that much of the discussion below will benefit from having those papers in front of you.