The Potts model and the Tutte polynomial

2000/03/01 by Dominic Welsh, Criel Merino · 3 citations
Mathematics · #Advanced Combinatorial Mathematics #Stochastic processes and statistical mechanics #Mathematical Dynamics and Fractals #Potts model #Tutte polynomial #Chiral Potts curve #Partition function (quantum field theory) #Mathematics #Combinatorics #Polynomial #Square lattice #Lattice (music) #Chromatic polynomial #Discrete mathematics #Statistical physics #Ising model #Graph #Physics #Mathematical analysis #Quantum mechanics

paper · doi:10.1063/1.533181

openalex publication_date 2000/03/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/18

Abstract

This is an invited survey on the relation between the partition function of the Potts model and the Tutte polynomial. On the assumption that the Potts model is more familiar we have concentrated on the latter and its interpretations. In particular we highlight the connections with Abelian sandpiles, counting problems on random graphs, error correcting codes, and the Ehrhart polynomial of a zonotope. Where possible we use the mean field and square lattice as illustrations. We also discuss in some detail the complexity issues involved.

Citations

• Decompositions of Rational Convex Polytopes
• The statistics of dimers on a lattice
• Facing up to arrangements: face-count formulas for partitions of space by hyperplanes
• On the computational complexity of the Jones and Tutte polynomials
• Chip-firing Games on Graphs
• Acyclic orientations of graphs

Cited by

• Computing the Tutte Polynomial in Vertex-Exponential Time
• Computing Tutte Polynomials
• Tutte polynomial [wikipedia]