Topics on abelian spin models and related problems

Abstract

In these notes, we discuss a selection of topics on several models of planar statistical mechanics. We consider the Ising, Potts, and more generally abelian spin models; the discrete Gaussian free field; the random cluster model; and the six-vertex model. Emphasis is put on duality, order, disorder and spinor variables, and on mappings between these models.

arXiv comment28 pages

References in corpus (7)

• The Random-Cluster Model
• A variational principle for domino tilings
• Discrete Riemann Surfaces and the Ising model
• Discretely Holomorphic Parafermions and Integrable Loop Models
• Domino tilings and the six-vertex model at its free fermion point
• Holomorphic Parafermions in the Potts model and SLE
• Homology of Fortuin-Kasteleyn clusters of Potts models on the torus

Cited by in corpus (3)

• An elementary proof of phase transition in the planar XY model
• Asymptotics of height change on toroidal Temperleyan dimer models
• On the duality between height functions and continuous spin models