LOW-TEMPERATURE EXPANSION OF MATRIX MODELS

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 1/2 nu- 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-->infinity, which is especially clear in the low temperature expansion; we prove that in this limit the dependence of the model on nu becomes trivial.