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 $\nu$ 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 $\nu \to \infty$, which is especially clear in the low temperature expansion; we prove that in this limit the dependence of the model on $\nu$ becomes trivial.

10 pp. and 5 figures (included), TeX + harvmac, PUPT-1384

References in corpus (4)

• Renormalization Group Approach to Matrix Models
• Induced QCD at Large N
• A naive matrix-model approach to two-dimensional quantum gravity coupled to matter of arbitrary central charge
• Perturbative analysis of an n-Ising model on a random surface

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