Gonihedric (and Fuki-Nuke) order

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 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 si s j
summed over planes replace a sum over spin values si . 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.