Low Temperature Expansion of Matrix Models

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 $ν$ uncoupled Ising models---which have central charge $ν/2$---we work out the expansion to sixth order for $ν$ = 1, 2, and 3. Analyzing the series by the ratio method, we exhibit the spin-ordering phase transition. We discuss the limit $ν\rightarrow \infty$, which is especially clear in the low temperature expansion; we prove that in this limit the dependence of the model on $ν$ becomes trivial.