A disorder analysis of the Ising model

TL;DR

This paper explores the concept of disorder parameters in the Ising model, demonstrating their construction and behavior in a duality context through an exactly solvable 2D case, linking lattice gauge theories and statistical mechanics.

Contribution

It provides a detailed analysis of disorder parameters in the 2D Ising model, illustrating their construction and properties in a duality framework, extending ideas from lattice QCD studies.

Findings

Disorder parameters can be explicitly constructed in the 2D Ising model.

The behavior of these parameters confirms duality properties.

The study offers insights into monopole condensation analogies in statistical mechanics.

Abstract

Lattice studies of monopole condensation in QCD are based on the construction of a disorder parameter, a creation operator of monopoles which is written in terms of the gauge fields. This procedure is expected to work for any system which presents duality. We check it on the Ising model in 2d, which is exactly solvable. The output is an amusing exercise in statistical mechanics.