Critical behaviour of the three-dimensional gonihedric Ising Model

TL;DR

This paper investigates the phase structure of the three-dimensional gonihedric Ising model using CVM and Monte Carlo simulations, revealing its universality class matches that of the standard 3D Ising model.

Contribution

It provides a detailed analysis of the gonihedric Ising model's phase diagram and confirms its universality class through combined computational methods.

Findings

Phase diagram aligns with the 3D Ising model

Model shares universality class with the standard 3D Ising model

CVM and Monte Carlo results are consistent

Abstract

We use the cluster variation method (CVM) and Monte Carlo simulations to investigate the phase structure of the 3d gonihedric Ising actions defined by Savvidy and Wegner. This model corresponds to the usual three-dimensional cubic Ising model with nearest, next to the nearest, and plaquette interactions in the region with degenerate lamellar ground states. The picture of the phase diagram given by the CVM is in good agreement with the results of Monte Carlo simulations, and it is shown that the gonihedric model is in the same universality class of the ordinary three-dimensional Ising model.