Duality of a Generalized Gauge Invariant Ising Model on Random Surfaces

TL;DR

This paper introduces a generalized gauge invariant Ising model on random surfaces, explores its duality properties, and shows it reduces to known models in special cases, contributing to the understanding of gauge theories on complex topologies.

Contribution

It proposes a new generalized gauge invariant Ising model on random surfaces and analyzes its self-duality and reduction to known models.

Findings

The model is self-dual on self-dual lattices.

In special cases, it simplifies to known solvable Ising models.

The dual transformation reveals key symmetry properties.

Abstract

A generalized gauge invariant Ising model on random surfaces with non-trivial topology is proposed and investigated with the dual transformation. It is proved that the model is self-dual in case of a self-dual lattice. In special cases the model reduces to the known solvable Ising-type models.