Probability measures and Hamiltonian models on Bethe lattices. I. Properties and construction of MRT probability measures

Abstract

The properties of one-step Markov, rotationally and m-step (m=1 or 2) translationally invariant (MRT) probability measures on q-state-site (qSS) Bethe lattices are studied. A theorem is proven, which completely defines such measures in terms of m(q2+q) fundamental probabilities. These are explicitly calculated for any MRT–qSS Hamiltonian model. As a consequence of our approach, the dychotomy between alternative solutions of Hamiltonian models on Bethe lattices is solved.

Identifiers

DOI

10.1063/1.526080

Citations and references