Macroscopic Degeneracy and order in the 3d plaquette Ising model

TL;DR

This paper investigates the 3d plaquette Ising model, revealing macroscopic degeneracy, layered order, and unique finite-size effects, confirmed through multicanonical simulations.

Contribution

It demonstrates the existence of layered 'fuki-nuke' order in the 3d plaquette Ising model and analyzes the impact of degeneracy on phase transition scaling.

Findings

Layered 'fuki-nuke' order persists in the anisotropic limit.

Macroscopic degeneracy affects finite-size scaling at the transition.

Simulations confirm layered order despite symmetry constraints.

Abstract

The purely plaquette 3d Ising Hamiltonian with the spins living at the vertices of a cubic lattice displays several interesting features. The symmetries of the model lead to a macroscopic degeneracy of the low-temperature phase and prevent the definition of a standard magnetic order parameter. Consideration of the strongly anisotropic limit of the model suggests that a layered, "fuki-nuke" order still exists and we confirm this with multicanonical simulations. The macroscopic degeneracy of the low-temperature phase also changes the finite-size scaling corrections at the first-order transition in the model and we see this must be taken into account when analysing our measurements.