Solvable statistical models on a random lattice

Details Solvable statistical models on a random lattice Solvable statistical models on a random lattice

1995-09-22

arxiv.org/abs/hep-th/9509124v4

Nucl.Phys.Proc.Suppl. 45A (1996) 13-28

Physics

High Energy Physics

High Energy Physics - Theory

Talk presented at the Conference on recent developments in statistical mechanics and quantum field theory (10 - 12 April 1995)

Scientific paper

We give a sequence of equivalent formulations of the $ADE$ and $\hat A\hat D\hat E$ height models defined on a random triangulated surface: random surfaces immersed in Dynkin diagrams, chains of coupled random matrices, Coulomb gases, and multicomponent Bose and Fermi systems representing soliton $\tau$-functions. We also formulate a set of loop-space Feynman rules allowing to calculate easily the partition function on a random surface with arbitrary topology. The formalism allows to describe the critical phenomena on a random surface in a unified fashion and gives a new meaning to the $ADE$ classification.

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