Asymptotics of partition functions in a fermionic matrix model and of related $q$-polynomials

TL;DR

This paper investigates the asymptotic behavior of the partition function in a fermionic matrix model, revealing connections to $q$-polynomials and developing new asymptotic methods involving theta functions.

Contribution

It introduces a novel asymptotic analysis of a fermionic matrix model's partition function and develops a new method for analyzing general $q$-polynomials.

Findings

Asymptotic formulas involve theta functions and derivatives.

Explicit connection between partition functions and Stieltjes-Wigert polynomials.

Development of a new asymptotic method for $q$-polynomials.

Abstract

In this paper, we study asymptotics of the thermal partition function of a model of quantum mechanical fermions with matrix-like index structure and quartic interactions. This partition function is given explicitly by a Wronskian of the Stieltjes-Wigert polynomials. Our asymptotic results involve the theta function and its derivatives. We also develop a new asymptotic method for general $q$-polynomials.