Cayley Trees and Bethe Lattices, a concise analysis for mathematicians and physicists

Details Cayley Trees and Bethe Lattices, a concise analysis for mathematicians and physicists Cayley Trees and Bethe Lattices, a concise analysis for mathematicians and physicists

2011-09-30

arxiv.org/abs/1109.6725v2

Physica A, 391, 3417 (2012)

Physics

Condensed Matter

Statistical Mechanics

10 pages, 2 figures

Scientific paper

10.1016/j.physa.2012.01.038

We review critically the concepts and the applications of Cayley Trees and Bethe Lattices in statistical mechanics in a tentative effort to remove widespread misuse of these simple, but yet important - and different - ideal graphs. We illustrate, in particular, two rigorous techniques to deal with Bethe Lattices, based respectively on self-similarity and on the Kolmogorov consistency theorem, linking the latter with the Cavity and Belief Propagation methods, more known to the physics community.

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