Low Temperature Expansion of Matrix Models

TL;DR

This paper develops a systematic low-temperature expansion for matrix models coupled with matter, specifically analyzing Ising models, and identifies phase transitions and the behavior as the number of models grows large.

Contribution

It provides a detailed sixth-order expansion for multiple Ising models coupled to matrix models and analyzes the phase transition and large- u limit.

Findings

Identified spin-ordering phase transition via ratio analysis.

Derived the low-temperature expansion up to sixth order for u=1,2,3.

Showed the trivial dependence of the model on u in the large- u limit.

Abstract

We show how to expand the free energy of a matrix model coupled to arbitrary matter in powers of the matter coupling constant. Concentrating on $\nu$ uncoupled Ising models---which have central charge $\nu/2$---we work out the expansion to sixth order for $\nu$ = 1, 2, and 3. Analyzing the series by the ratio method, we exhibit the spin-ordering phase transition. We discuss the limit $\nu \rightarrow \infty$, which is especially clear in the low temperature expansion; we prove that in this limit the dependence of the model on $\nu$ becomes trivial.