Gonihedric (and Fuki-Nuke) Order

TL;DR

This paper investigates the complex ordering phenomena in 3D Gonihedric Ising models with plaquette interactions, proposing a planar magnetization as a potential order parameter and validating it through Monte Carlo simulations.

Contribution

It introduces a novel planar magnetization order parameter for the isotropic Gonihedric model and demonstrates its effectiveness via simulations, extending understanding of its phase transition behavior.

Findings

Planar magnetization serves as an effective order parameter.

Anisotropic Fuki-Nuke model maps to stacked 2D Ising models.

Monte Carlo simulations support the proposed order parameter.

Abstract

A 3D Ising model with a purely plaquette, 4-spin interaction displays a planar flip symmetry intermediate between a global and a gauge symmetry and as a consequence has a highly degenerate low temperature phase and no standard magnetic order parameter. This plaquette Hamiltonian is a particular case of a family of 3D Gonihedric Ising models defined by Savvidy and Wegner. An anisotropic variant of the the purely plaquette Gonihedric model, originally discussed as the "Fuki-Nuke" model by Suzuki, is non-trivially equivalent to a stack of 2D Ising models, each of which can magnetize independently at the phase transition point. Consideration of this anisotropic model suggests that a suitable order parameter in the isotropic case may also be constructed using a form of planar magnetization, in which nearest neighbour correlators summed over planes replace a sum over spin values. We conduct Monte-Carlo simulations to investigate this and related candidate order parameters in a toy model of Gonihedric ground states, the Fuki-Nuke model and the isotropic plaquette Gonihedric model itself.