A Gauge Invariant Dual Gonihedric 3D Ising Model

TL;DR

This paper explores dual formulations of the 3D gonihedric Ising model, revealing gauge invariance and equivalences to other models, supported by Monte Carlo simulations.

Contribution

It establishes the gauge invariance in dual gonihedric Ising models and links different formulations through detailed transformations and simulations.

Findings

Dual formulations are related by decoration/iteration transformation.

Gauge invariance ensures equivalence to an anisotropic Ashkin-Teller model.

Monte Carlo simulations support the theoretical equivalences.

Abstract

We note that two formulations of dual gonihedric Ising models in 3d, one based on using Wegner's general framework for duality to construct a dual Hamiltonian for codimension one surfaces, the other on constructing a dual Hamiltonian for two-dimensional surfaces, are related by a variant of the standard decoration/iteration transformation. The dual Hamiltonian for two-dimensional surfaces contains a mixture of link and vertex spins and as a consequence possesses a gauge invariance which is inherited by the codimension one surface Hamiltonian. This gauge invariance ensures the latter is equivalent to a third formulation, an anisotropic Ashkin-Teller model. We describe the equivalences in detail and discuss some Monte-Carlo simulations which support these observations.