Gonihedric 3D Ising Actions

TL;DR

This paper explores a generalized 3D Ising model with complex interactions, analyzing its phase diagram and critical behavior using mean field and Monte Carlo methods, revealing a highly degenerate vacuum state and critical exponents.

Contribution

It introduces a generalized Ising action with multiple interaction terms and studies its phase structure and critical properties through combined analytical and numerical techniques.

Findings

Identified phase diagram features of the model.

Determined magnetic critical exponents.

Revealed a highly degenerate vacuum state.

Abstract

We investigate a generalized Ising action containing nearest neighbour, next to nearest neighbour and plaquette terms that has been suggested as a potential string worldsheet discretization on cubic lattices by Savvidy and Wegner. We use both mean field techniques and Monte-Carlo simulations to sketch out the phase diagram. The Gonihedric (Savvidy-Wegner) model has a symmetry that allows any plane of spins to be flipped with zero energy cost, which gives a highly degenerate vacuum state. We choose boundary conditions in the simulations that eliminate this degeneracy and allow the definition of a simple ferromagnetic order parameter. This in turn allows us to extract the magnetic critical exponents of the system.