Interaction Hierarchy

Abstract

We analyse a new class of statistical systems, which simulate different systems of random surfaces on a lattice. Geometrical hierarchy of the energy functionals on which these theories are based produces corresponding hierarchy of the surface dynamics and of the phase transitions. We specially consider 3D gonihedric system and have found that it is equivalent to the propagation of almost free 2D Ising fermions. We construct dual statistical system with new matchbox spin variable $G_{\xi }$, high temperature expansion of which equally well describe these surfaces.

11 pages,Latex,Crete-TH-March-1994

References in corpus (7)

• Geometrical String and Spin Systems
• Gonihedric String and Asymptotic Freedom
• Self-Avoiding Gonihedric Srting and Spin Systems
• String fine tuning
• Critical and Topological Properties of Cluster Boundaries in the $3d$ Ising Model
• On subdivision invariant actions for random surfaces
• A Lower Estimate for the Modified Steiner Functional

Cited by in corpus (32)

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• Quantum mechanical and information theoretic view on classical glass transitions
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• Low temperature expansion of the gonihedric Ising model
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• The Phase Diagram of the Gonihedric 3d Ising Model via CVM
• String tension in gonihedric 3D Ising models
• Gonihedric (and Fuki-Nuke) Order
• Phase structure of four-dimensional gonihedric spin system
• Multi-criticality of the three-dimensional Ising model with plaquette interactions: An extension of Novotny's transfer-matrix formalism
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• Three-dimensional gonihedric spin system
• Alternative actions for quantum gravity and the intrinsic rigidity of the spacetime
• Stability of Yang Mills Vacuum State
• New Random Ordered Phase in Isotropic Models with Many-body Interactions
• The spectrum of a transfer matrix for loops
• The Dual Gonihedric 3D Ising Model
• Planar ordering in the plaquette-only gonihedric Ising model
• Gonihedric String Equation II
• The Gonihedric Paradigm Extensions of the Ising Model
• Fixed boundary conditions analysis of the 3d Gonihedric Ising model with $\kappa =0$
• Quantum gravity with linear action. Intrinsic rigidity of spacetime
• Gonihedric String Equation
• Yang-Mills Effective Lagrangian. Contribution of Leutwyler Zero Mode Chromons
• (Four) Dual Plaquette 3D Ising Models
• Gonihedric Ising Actions
• The Spectrum of the Loop Transfer Matrix on Finite Lattice
• Three-dimensional Gonihedric Potts model
• The QCD string and the generalised wave equation
• Finite size analysis of the 3D gonihedric Ising model with k=0