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Bethe lattice
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{{Short description|Regular infinite tree structure used in statistical mechanics}} {{redirect|Cayley tree|finite trees with equal-length root-to-leaf paths|ordered Bell number}} {{expert|Mathematics|date=March 2025|reason=Multiple errors, unexplained notation, inconsistent notation, confusing claims; see talk page for details}} [[Image:Reseau de Bethe.svg|thumb|225px|right|A Bethe lattice with coordination number ''z'' = 3]] In [[statistical mechanics]] and [[mathematics]], the '''Bethe lattice''' (also called a '''regular tree''') is an infinite [[symmetric graph|symmetric]] [[Regular graph|regular]] [[tree (graph theory)|tree]] where all vertices have the same number of neighbors. The Bethe lattice was introduced into the physics literature by [[Hans Bethe]] in 1935. In such a graph, each node is connected to ''z'' neighbors; the number ''z'' is called either the [[coordination number]] or the [[degree (graph theory)|degree]], depending on the field. Due to its distinctive topological structure, the statistical mechanics of [[lattice model (physics)|lattice models]] on this graph are often easier to solve than on other lattices. The solutions are related to the often used [[Bethe ansatz]] for these systems.
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