(Four) Dual Plaquette 3D Ising Models

TL;DR

This paper explores the classical spin version of a non-standard dual Hamiltonian related to the 3D plaquette Ising model, connecting it to fracton models and various dual formulations.

Contribution

It investigates the properties of a classical dual Hamiltonian involving three flavors of spins, expanding understanding of dualities in 3D plaquette Ising models.

Findings

Analysis of the classical dual Hamiltonian reveals its relation to Ashkin-Teller-like models.

Discussion of dual formulations involving link, vertex, and non-Ising spins.

Insights into the connection between the classical model and fracton-related quantum models.

Abstract

A characteristic feature of the 3d plaquette Ising model is its planar subsystem symmetry. The quantum version of this model has been shown to be related via a duality to the X-Cube model, which has been paradigmatic in the new and rapidly developing field of fractons. The relation between the 3d plaquette Ising and the X-Cube model is similar to that between the 2d quantum transverse spin Ising model and the Toric Code. Gauging the global symmetry in the case of the 2d Ising model and considering the gauge invariant sector of the high temperature phase leads to the Toric Code, whereas gauging the subsystem symmetry of the 3d quantum transverse spin plaquette Ising model leads to the X-Cube model. A non-standard dual formulation of the 3d plaquette Ising model which utilises three flavours of spins has recently been discussed in the context of dualising the fracton-free sector of the X-Cube model. In this paper we investigate the classical spin version of this non-standard dual Hamiltonian and discuss its properties in relation to the more familiar Ashkin-Teller-like dual and further related dual formulations involving both link and vertex spins and non-Ising spins.