Planar ordering in the plaquette-only gonihedric Ising model

TL;DR

This study uses multicanonical simulations to confirm planar order in the low-temperature phase of the 3D plaquette gonihedric Ising model and introduces new order parameters to distinguish phases.

Contribution

It defines novel order parameters based on anisotropic limits and clarifies the true nature of phase transition behavior in the model.

Findings

Confirmed planar, fuki-nuke type order in low-temperature phase

Standard magnetic susceptibility is an artefact, not a proper order parameter

Established new order parameters for phase distinction

Abstract

In this paper we conduct a careful multicanonical simulation of the isotropic $3d$ plaquette ("gonihedric") Ising model and confirm that a planar, fuki-nuke type order characterises the low-temperature phase of the model. From consideration of the anisotropic limit of the model we define a class of order parameters which can distinguish the low- and high-temperature phases in both the anisotropic and isotropic cases. We also verify the recently voiced suspicion that the order parameter like behaviour of the standard magnetic susceptibility $\chi_m$ seen in previous Metropolis simulations was an artefact of the algorithm failing to explore the phase space of the macroscopically degenerate low-temperature phase. $\chi_m$ is therefore not a suitable order parameter for the model.