Solvable statistical models on a random lattice

Ivan K. Kostov

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arXiv · hep-th/9509124

Solvable statistical models on a random lattice

Ivan K. Kostov

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Abstract

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 $τ$-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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Ivan K. Kostov. 1995-10-03. Solvable statistical models on a random lattice. https://arxiv.org/abs/hep-th/9509124

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