The Dual Gonihedric 3D Ising Model

TL;DR

This paper studies the dual of a 3D Gonihedric Ising model, revealing its large ground state degeneracy, first order phase transition, and complex dynamical behavior through theoretical analysis and Monte Carlo simulations.

Contribution

It introduces the dual anisotropic Ashkin-Teller model of the Gonihedric Ising model and analyzes its phase transition and ground state properties.

Findings

The dual model exhibits a first order phase transition.

Ground state degeneracy persists in the low temperature phase.

Monte Carlo simulations confirm theoretical predictions.

Abstract

We investigate the dual of the kappa=0 Gonihedric Ising model on a 3D cubic lattice, which may be written as an anisotropically coupled Ashkin-Teller model. The original kappa=0 Gonihedric model has a purely plaquette interaction, displays a first order transition and possesses a highly degenerate ground state. We find that the dual model admits a similar large ground state degeneracy as a result of the anisotropic couplings and investigate the coupled mean field equations for the model on a single cube. We also carry out Monte Carlo simulations which confirm a first order phase transition in the model and suggest that the ground state degeneracy persists throughout the low temperature phase. Some exploratory cooling simulations also hint at non-trivial dynamical behaviour.