Might there be a good reference on the interaction of number theory with statistical physics? I am particularly interested in innovations in number theory that have led to breakthroughs in statistical physics.


One such result that I am aware of is the Lee-Yang theorem. Marc Kac apparently used insights from Pólya's analysis of the Riemann Zeta function [2] in order to come up with an early proof of the Lee-Yang theorem(aka Lee-Yang Circle theorem) which states that the zeros of certain partition functions lie on the unit circle [1].


At present, I am more familiar with parallel developments such as the correspondence between Gaussian Unitary Ensembles(GUEs) and Montgomery's pair correlation conjecture [3].


References:
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1. Knauf, Andreas (1999), "Number theory, dynamical systems and statistical mechanics", Reviews in Mathematical Physics, 11 (8): 1027–1060, CiteSeerX 10.1.1.184.8685
2. Pólya, G.: Collected Papers, Vol. II: Locations of Zeros (R.P. Boas, ed.).
Cambridge: M.I.T. Press 1974
3. Montgomery, Hugh L. (1973), "The pair correlation of zeros of the zeta function", Analytic number theory, Proc. Sympos. Pure Math., XXIV, Providence, R.I.: American Mathematical Society



Innovations in number theory leading to breakthroughs in statistical mechanics
1. The paper “The reasonable and unreasonable effectiveness of number theory in statistical mechanics” by George Andrews comes to mind. It is a nice survey that mentions some of the more striking appearances of number-theoretic results in statistical mechanics, such as the Rogers-Ramanujan identities and their connection to the hard hexagon model. It appeared in the book The Unreasonable Effectiveness of Number Theory (Ed. Stefan A. Burr, Amer. Math. Soc. 1993), which has a few other nice essays by different authors.
2. The journal [Communications in Number Theory and Physics](https://www.intlpress.com/site/pub/pages/journals/items/cntp/_home/_main/index.php) might have some relevant material.


