Geometrically Constrained Statistical Models on Fixed and Random Lattices: From Hard Squares to Meanders

Details Geometrically Constrained Statistical Models on Fixed and Random Lattices: From Hard Squares to Meanders Geometrically Constrained Statistical Models on Fixed and Random Lattices: From Hard Squares to Meanders

2002-11-26

arxiv.org/abs/cond-mat/0211591v1

Physics

Condensed Matter

Statistical Mechanics

47 pages, 19 figures, tex, harvmac, epsf

Scientific paper

We review various combinatorial applications of field theoretical and matrix model approaches to equilibrium statistical physics involving the enumeration of fixed and random lattice model configurations. We show how the structures of the underlying lattices, in particular their colorability properties, become relevant when we consider hard-particles or fully-packed loop models on them. We show how a careful back-and-forth application of results of two-dimensional quantum gravity and matrix models allows to predict critical universality classes and consequently exact asymptotics for various numbers, counting in particular hard object configurations on fixed or random lattices and meanders.

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