Geometrical String and Spin Systems

Abstract

We formulate a new geometrical string on the euclidean lattice. It is possible to find such spin systems with local interaction which reproduce the same surface dynamics.In the three-dimensional case this spin system is a usual Ising ferromagnet with additional diagonal antiferromagnetic interaction and with specially adjusted coupling constants. In the four-dimensional case the spin system coincides with the gauge Ising system with an additional double-plaquette interaction and also with specially tuned coupling constants. We extend this construction to random walks and random hypersurfaces (membrane and p-branes) of high dimensionality. We compare these spin systems with the eight-vertex model and BNNNI models.

10 pages, Latex,Crete-TH-5-July-1993

References in corpus (1)

• String fine tuning

Cited by in corpus (52)

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• Multicanonical analysis of the plaquette-only gonihedric Ising model and its dual
• Four-dimensional gonihedric gauge spin system
• Exact solutions to plaquette Ising models with free and periodic boundaries
• 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
• Fracton-like phases from subsystem symmetries
• Stability of Yang Mills Vacuum State
• Three-dimensional gonihedric spin system
• Crystallization of a supercooled liquid and of a glass - Ising model approach
• Linked Cluster Expansions via Hypergraph Decompositions
• The Dual Gonihedric 3D Ising Model
• The spectrum of a transfer matrix for loops
• The Gonihedric Paradigm Extensions of the Ising Model
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