Solvable statistical models on a random lattice
Abstract
Description
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.
Talk presented at the Conference on recent developments in statistical mechanics and quantum field theory (10 - 12 April 1995), Trieste, Italy; 16 pages, latex, no figures, espcrc2.tex; Eq. (39) corrected
Talk presented at the Conference on recent developments in statistical mechanics and quantum field theory (10 - 12 April 1995), Trieste, Italy; 16 pages, latex, no figures, espcrc2.tex; Eq. (39) corrected