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 χm seen in previous Metropolis simulations was an artefact of the algorithm failing to explore the phase space of the macroscopically degenerate low-temperature phase. χm is therefore not a suitable order parameter for the model.
Highlights
The 3d plaquette (“gonihedric”) Ising Hamiltonian displays an unusual planar flip symmetry, leading to an exponentially degenerate low-temperature phase and non-standard scaling at its first-order phase transition point [1, 2]
Metropolis algorithm [3] have indicated that the magnetic ordering remains a fuki-nuke type planar layered ordering, which can be shown rigorously to occur in the extreme anisotropic limit when the plaquette coupling in one direction is set to zero [4, 5, 6] by mapping the model onto a stack of 2d Ising models
For κ = 0 parallel, non-intersecting planes of spins may be flipped in the ground state at zero energy cost, leading to a 3 × 22L ground-state degeneracy on an L × L × L cubic lattice which is broken at finite temperature [8]
Summary
The 3d plaquette (“gonihedric”) Ising Hamiltonian displays an unusual planar flip symmetry, leading to an exponentially degenerate low-temperature phase and non-standard scaling at its first-order phase transition point [1, 2]. For the κ = 0 plaquette Hamiltonian of Eq (1), on the other hand, the planar flip symmetry persists throughout the low-temperature phase and extends to intersecting planes of spins. This results in a macroscopic low-temperature phase degeneracy of 23L and non-standard corrections to finite-size scaling at the first-order transition displayed by the model [1, 2]. The absence of a local gauge-like symmetry means that observing the behaviour of Wilson-loop type observables, as in a gauge theory, is not appropriate
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