Bethe lattice

A Bethe lattice, introduced by Hans Bethe in 1935, is an infinite connected cycle-free graph where each node is connected to z neighbours, where z is called the coordination number. It is a rooted tree, with all other nodes arranged in shells around the root node, also called the origin of the lattice. The number of nodes in the kth shell is given by A Bethe lattice, introduced by Hans Bethe in 1935, is an infinite connected cycle-free graph where each node is connected to z neighbours, where z is called the coordination number. It is a rooted tree, with all other nodes arranged in shells around the root node, also called the origin of the lattice. The number of nodes in the kth shell is given by In some situations the definition is modified to specify that the root node has z − 1 neighbors. Due to its distinctive topological structure, the statistical mechanics of lattice models on this graph are often exactly solvable. The solutions are related to the often used Bethe approximation for these systems.