Matrix Models on Large Graphs

Details Matrix Models on Large Graphs Matrix Models on Large Graphs

1993-05-11

arxiv.org/abs/hep-th/9305041v1

Nucl.Phys. B410 (1993) 377-394

Physics

High Energy Physics

High Energy Physics - Theory

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

Scientific paper

10.1016/0550-3213(93)90439-V

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.

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