Gonihedric (and Fuki-Nuke) Order

Abstract

A 3D Ising model with a purely plaquette, 4-spin interaction displays a planar flip symmetry intermediate between a global and a gauge symmetry and as a consequence has a highly degenerate low temperature phase and no standard magnetic order parameter. This plaquette Hamiltonian is a particular case of a family of 3D Gonihedric Ising models defined by Savvidy and Wegner. An anisotropic variant of the the purely plaquette Gonihedric model, originally discussed as the "Fuki-Nuke" model by Suzuki, is non-trivially equivalent to a stack of 2D Ising models, each of which can magnetize independently at the phase transition point. Consideration of this anisotropic model suggests that a suitable order parameter in the isotropic case may also be constructed using a form of planar magnetization, in which nearest neighbour correlators summed over planes replace a sum over spin values. We conduct Monte-Carlo simulations to investigate this and related candidate order parameters in a toy model of Gonihedric ground states, the Fuki-Nuke model and the isotropic plaquette Gonihedric model itself.

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Cited by in corpus (14)

• Classification of subsystem symmetry-protected topological phases
• Correlation function diagnostics for type-I fracton phases
• Strong planar subsystem symmetry-protected topological phases and their dual fracton orders
• Plaquette Ising models, degeneracy and scaling
• Overlap and activity glass transitions in plaquette spin models with hierarchical dynamics
• Classifying local fractal subsystem symmetry protected topological phases
• Exact solutions to plaquette Ising models with free and periodic boundaries
• Planar ordering in the plaquette-only gonihedric Ising model
• The Gonihedric Paradigm Extensions of the Ising Model
• Geometric clusters in the overlap of the Ising model
• (Four) Dual Plaquette 3D Ising Models
• Macroscopic Degeneracy and order in the 3d plaquette Ising model
• Order formation processes of complex systems including different parity order parameters
• Stretched exponentials and tensionless glass in the plaquette Ising model