Topics on abelian spin models and related problems

TL;DR

This paper reviews various planar statistical mechanics models, focusing on duality, mappings, and key variables, to deepen understanding of their interrelations and fundamental properties.

Contribution

It provides a comprehensive overview of abelian spin models and related models, highlighting dualities and mappings that connect different statistical mechanics systems.

Findings

Exploration of duality relations among models

Analysis of order, disorder, and spinor variables

Connections between different models via mappings

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.