The spectrum of a transfer matrix for loops

Abstract

We study the spectral properties of the transfer matrix for a gonihedric random surface model on a three-dimensional lattice. The transfer matrix is indexed by generalized loops in a natural fashion and is invariant under a group of motions in loop-space. The eigenvalues of the transfer matrix can be evaluated exactly in terms of the partition function, the internal energy and the correlation functions of the two-dimensional Ising model and the corresponding eigenfunctions are explicit functions on loop-space.

Latex2e 13 pages

References in corpus (2)

• Low temperature expansion of the gonihedric Ising model
• Loop transfer matrix and gonihedric loop diffusion

Cited by in corpus (5)

• Quantum mechanical and information theoretic view on classical glass transitions
• Gonihedric (and Fuki-Nuke) Order
• Exact solutions to plaquette Ising models with free and periodic boundaries
• The Gonihedric Paradigm Extensions of the Ising Model
• Three-dimensional Gonihedric Potts model