The Potts and random-cluster models
Geoffrey R. Grimmett
TL;DR
This paper explores the deep connections between the Tutte polynomial and various statistical physics models, including the Ising, Potts, and random-cluster models, highlighting their historical development and mathematical relationships.
Contribution
It provides a concise overview of the links between the Tutte polynomial and key models in statistical mechanics, emphasizing their interconnectedness.
Findings
Tutte polynomial relates to the partition functions of these models
Historical timeline of models and polynomial development
Mathematical connections between models and graph invariants
Abstract
This is a short account of connections between the Tutte polynomial and the Ising, Potts, and random-cluster models. The four principal elements are the Ising model of 1925, the Tutte polynomial of 1947, the Potts model of 1952, and the random-cluster model of 1972.
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Taxonomy
TopicsStochastic processes and statistical mechanics · Theoretical and Computational Physics · Markov Chains and Monte Carlo Methods