Planar ordering in the plaquette-only gonihedric Ising model

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.

Comments: The discussion of the treatment of errors is expanded, the description of the variable transformation in the anisotropic case is clarified, various minor typos are fixed and some references have been added