Interaction hierarchy

1994/09/05 by George Savvidy, G. K. Savvidy, Konstantin Savvidy +1 · 2 citations
Mathematics · Physics and Astronomy · #Class (philosophy) #Computer science #Construct (python library) #Fermion #Geometry #Hierarchy #Ising model #Lattice (music) #Markov Chains and Monte Carlo Methods #Mathematics #Phase transition #Physics #Quantum mechanics #Statistical mechanics #Statistical physics #Stochastic processes and statistical mechanics #Surface (topology) #Theoretical and Computational Physics #Theoretical physics #hep-th

paper · pdf · doi:10.1016/0370-2693(94)90984-9

published as Phys.Lett.B337:333-339,1994 · 11 pages,Latex,Crete-TH-March-1994

arxiv created 1994/09/05 · openalex publication_date 1994/10/01 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

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_ξ, high temperature expansion of which equally well describe these surfaces.

Citations

• Duality in Generalized Ising Models and Phase Transitions without Local Order Parameters
• Beitrag zur Theorie des Ferromagnetismus
• Crystal Statistics. I. A Two-Dimensional Model with an Order-Disorder Transition
• Critical and topological properties of cluster boundaries in the 3D Ising model
• On the Total Curvature of Knots

Cited by

• Four-dimensional gonihedric gauge spin system
• Geometrical string and dual spin systems