Matrix Models on Large Graphs

Abstract

We consider the spherical limit of multi-matrix models on regular target graphs, for instance single or multiple Potts models, or lattices of arbitrary dimension. We show, to all orders in the low temperature expansion, that when the degree of the target graph $\Delta \to \infty$, the free energy becomes independent of the target graph, up to simple transformations of the matter coupling constant. Furthermore, this universal free energy contains contributions only from those surfaces which are made up of ``baby universes'' glued together into trees, all non-universal and non-tree contributions being suppressed by inverse powers of $\Delta$. Each order of the free energy is put into a simple, algebraic form.

19pp. (uses harvmac and epsf), PUPT-1398

References in corpus (2)

• A naive matrix-model approach to two-dimensional quantum gravity coupled to matter of arbitrary central charge
• Low Temperature Expansion of Matrix Models

Cited by in corpus (10)

• Scaling in four dimensional quantum gravity
• A scenario for the c>1 barrier in non-critical bosonic strings
• New critical phenomena in 2d quantum gravity
• Multiple Ising Spins Coupled to 2d Quantum Gravity
• Softening of First-Order Phase Transition on Quenched Random Gravity Graphs
• Correlation Functions in the Multiple Ising Model Coupled to Gravity
• Square Gravity
• From Trees to Galaxies: The Potts Model on a Random Surface
• Solution of Potts-3 and Potts-\infty Matrix Models with the Equations of Motion Method
• A simple model of dimensional collapse