Gonihedric 3D Ising Actions

Abstract

We investigate a generalized Ising action containing nearest neighbour, next to nearest neighbour and plaquette terms that has been suggested as a potential string worldsheet discretization on cubic lattices by Savvidy and Wegner. We use both mean field techniques and Monte-Carlo simulations to sketch out the phase diagram. The Gonihedric (Savvidy-Wegner) model has a symmetry that allows any plane of spins to be flipped with zero energy cost, which gives a highly degenerate vacuum state. We choose boundary conditions in the simulations that eliminate this degeneracy and allow the definition of a simple ferromagnetic order parameter. This in turn allows us to extract the magnetic critical exponents of the system.

Latex plus 6 postscript figures bundled together with uufiles. The paper has been completely revised: a judicious choice of boundary conditions now allows the extraction of magnetic critical exponents. All the exponents, and even the critical temperature, appear close to those of the standard two-dimensional Ising model

References in corpus (4)

• Phase Transition in Lattice Surface Systems with Gonihedric Action
• Interaction Hierarchy. Gonihedric String and Quantum Gravity
• GEOMETRICAL STRING and DUAL SPIN SYSTEMS
• String tension in gonihedric 3D Ising models

Cited by in corpus (21)

• Plaquette Ising models, degeneracy and scaling
• Phase Transition in Lattice Surface Systems with Gonihedric Action
• Evidence for a first order transition in a plaquette 3d Ising-like action
• Non-Standard Finite-Size Scaling at First-Order Phase Transitions
• Low temperature expansion of the gonihedric Ising model
• Slow dynamics in the 3--D gonihedric model
• New critical behaviour of the three-dimensional Ising model with nearest-neighbor, next-nearest-neighbor and plaquette interactions
• The Phase Diagram of the Gonihedric 3d Ising Model via CVM
• String tension in gonihedric 3D Ising models
• Gonihedric (and Fuki-Nuke) Order
• Multicanonical analysis of the plaquette-only gonihedric Ising model and its dual
• Multi-criticality of the three-dimensional Ising model with plaquette interactions: An extension of Novotny's transfer-matrix formalism
• Dynamics of the two-dimensional gonihedric spin model
• Three-dimensional gonihedric spin system
• The Dual Gonihedric 3D Ising Model
• Planar ordering in the plaquette-only gonihedric Ising model
• Fixed boundary conditions analysis of the 3d Gonihedric Ising model with $\kappa =0$
• Critical behaviour of the three-dimensional gonihedric Ising Model
• (Four) Dual Plaquette 3D Ising Models
• Gonihedric Ising Actions
• Three-dimensional Gonihedric Potts model