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.Comment: 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 adde

Macroscopic degeneracy and order in the 3D plaquette Ising model

“…where to maintain a one-to-one correspondence between the σ and τ spin configurations on a periodic lattice the L 2 constraints of the τ -spins, L z=1 τ x,y,z = 1, must be satisfied and respected by an additional factor of 2 L×L in the partition function [10]. The resulting Hamiltonian when J x = J y = 1 is then…”

Plaquette Ising models, degeneracy and scaling

“…Since in references [36][37][38][39]41,42] we employed multicanonical simulations giving a flat energy distribution, reweighting techniques [64][65][66][67] can be used to get an estimator of the energy probability densities at different temperatures. β eqw is chosen systematically to minimise…”

“…The κ = 0 plaquette Hamiltonian, on the other hand, has a strong first-order phase transition [35] and recent high-precision multicanonical simulations [36][37][38][39] have revealed that it displays non-standard finite-size scaling properties at this transition. In the sequel we will describe how this non-standard scaling is a consequence of a macroscopic low-temperature phase degeneracy in the 3d plaquette Ising model and also discuss the implications of this degeneracy for the nature of the low-temperature phase and the definition of an order parameter [40][41][42]. Recent work on quantum spin versions of the plaquette model has also shown that the symmetries of the plaquette Hamiltonian and the low-temperature degeneracy are instrumental in the appearance of a novel form of topological defect, a fracton [43][44][45][46][47][48], and we sketch their appearance via a partial gauging construction using the quantum dual of the plaquette model.…”

The gonihedric paradigm extension of the Ising model

“…The other interesting property of the system is that the relaxation to the equilibrium state is very slow, like in spin glasses [20,39,41,42,43,44,45,46,51,54,52,55,56,57,58]. The reason is rooted in high symmetry of the system (3.9), its energy states are exponentially degenerated [17,18,19].…”