The Gonihedric Ising Model and Glassiness

TL;DR

This paper explores the Gonihedric 3D Ising model, focusing on its unique boundary properties, phase diagram, and glassy behavior, revealing insights into its equilibrium and non-equilibrium phenomena.

Contribution

It introduces and analyzes the Gonihedric Ising model, highlighting its distinctive boundary weighting and glassy dynamics, advancing understanding of complex lattice spin systems.

Findings

Planar boundaries can be created at zero energy cost.

The model exhibits a rich phase diagram with unique equilibrium properties.

Non-equilibrium analysis reveals glassy behavior and slow dynamics.

Abstract

The Gonihedric 3D Ising model is a lattice spin model in which planar Peierls boundaries between + and - spins can be created at zero energy cost. Instead of weighting the area of Peierls boundaries as the case for the usual 3D Ising model with nearest neighbour interactions, the edges, or "bends" in an interface are weighted, a concept which is related to the intrinsic curvature of the boundaries in the continuum. In these notes we follow a roughly chronological order by first reviewing the background to the formulation of the model, before moving on to the elucidation of the equilibrium phase diagram by various means and then to investigation of the non-equilibrium, glassy behaviour of the model.