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An Isaac Newton Institute Workshop

Graph Models of Mesoscopic Systems, Wave-Guides and Nano-Structures

Phase transitions on lattice graphs

Author: G. Grimmett (University of Cambridge)

Abstract

We explain the random-cluster (or FK) representation of the classical Potts/Ising models, when the underlying graph is a lattice. There is a continuum version of the random-cluster model that may be used to study the quantum Ising model with transverse field. A selection of open problems will be included.