Another Dual Gonihedric 3D Ising Model

TL;DR

This paper explores a new dual formulation of the 3D gonihedric Ising model, revealing a four-spin interaction model with gauge symmetry, analyzed through various computational methods.

Contribution

It introduces an alternative dual Hamiltonian with four-spin couplings and local gauge symmetry, expanding the understanding of gonihedric Ising models.

Findings

The new dual model exhibits a degenerate low-temperature phase.

It features anisotropic four-spin interactions with gauge symmetry.

Connections to the Ashkin-Teller model are discussed.

Abstract

The gonihedric Ising Hamiltonians defined in three and higher dimensions by Savvidy and Wegner provide an extensive, and little explored, catalogue of spin models on (hyper)cubic lattices with many interesting features. In three dimensions the kappa=0 gonihedric Ising model on a cubic lattice has been shown to possess a degenerate low-temperature phase and a first order phase transition, as well as interesting dynamical properties. The dual Hamiltonian to this may be written as an anisotropic Ashkin-Teller model and also has a degenerate low-temperature phase as a result of similar symmetries to the original plaquette action. It is possible to write an alternative dual formulation which utilizes three flavours of spins, rather than the two of the Ashkin-Teller model. This still possesses anisotropic couplings, but all the interaction terms are now four spin couplings and it acquires an additional, local gauge symmetry. We investigate this alternative dual Hamiltonian using zero temperature and mean-field methods together with Monte-Carlo simulations and discuss its properties and the relation to the Ashkin-Teller variant.