"Cayley tree" redirects here. For finite trees with equal-length root-to-leaf paths, see ordered Bell number.
A Bethe lattice with coordination number z = 3
In statistical mechanics and mathematics, the Bethe lattice (also called a regular tree) is an infinite connected cycle-free graph 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, depending on the field.
Due to its distinctive topological structure, the statistical mechanics of 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.
Bethelattice (also called a regular tree) is an infinite connected cycle-free graph where all vertices have the same number of neighbors. The Bethe lattice...
calculation Bethelattice, a regular infinite tree structure used in statistical mechanics Bravais lattice, a repetitive arrangement of atoms Lattice C, a compiler...
Hans Albrecht Bethe (German pronunciation: [ˈhans ˈbeːtə] ; July 2, 1906 – March 6, 2005) was a German-American theoretical physicist who made major contributions...
the Bethe ansatz is an ansatz for finding the exact wavefunctions of certain quantum many-body models, most commonly for one-dimensional lattice models...
mathematical terms as a model in percolation theory, which he analyses as a Bethelattice. The model includes active and latent failures. Active failures encompass...
= 0.59274621 ± 0.00000013. A limit case for lattices in high dimensions is given by the Bethelattice, whose threshold is at pc = 1/z − 1 for a coordination...
u}(3,Q)=1} because of the self-matching of triangulated lattices. Cayley tree (Bethelattice) with coordination number z : p c = 1 / ( z − 1 ) {\displaystyle...
Lattice QCD is a well-established non-perturbative approach to solving the quantum chromodynamics (QCD) theory of quarks and gluons. It is a lattice gauge...
ingredient in the proof of the Banach–Tarski paradox. More generally, the Bethelattice or Cayley tree is the Cayley graph of the free group on n {\displaystyle...
In physics, lattice gauge theory is the study of gauge theories on a spacetime that has been discretized into a lattice. Gauge theories are important...
Roch. These result links the extremality of the Ising model on the Bethelattice to a phase transition in the amount of data required for statistical...
Flory-Stockmayer theory of gelation, which equivalent to percolation on the Bethelattice and in fact represents the first paper in the percolation field. In...
ISSN 1042-9832. S2CID 6601396. Mézard, M.; Parisi, G. (2001). "The Bethelattice spin glass revisited". The European Physical Journal B. 20 (2): 217–233...
(1971). Combinatorics In Statistical Physics Hard Constraints and the BetheLattice: Adventures at the Interface of Combinatorics and Statistical Physics...
S2CID 9637234. D Dhar, S N Majumdar (1990). "Abelian sandpile model on the Bethelattice". Journal of Physics A: Mathematical and General. 23 (4333): 4333–4350...
spin 1/2 Heisenberg model in one dimension may be solved exactly using the Bethe ansatz. In the algebraic formulation, these are related to particular quantum...
Hamiltonian of the Heisenberg model was determined, by Hans Bethe using the Bethe ansatz. Now the term Bethe ansatz is used generally to refer to many ansatzes...
J.; Leath, P. L.; Reich, G. R. (1979), "Bootstrap percolation on a Bethelattice", Journal of Physics C: Solid State Physics, 12 (1): L31–L35, Bibcode:1979JPhC...
incorporated into the quantum inverse scattering method where the algebraic Bethe ansatz can be used to obtain explicit solutions. Examples of quantum integrable...
formed. The polymer we create follows the form of a Cayley tree or Bethelattice – known from the field of statistical mechanics. The number of branches...
glueballs, including their excitations, were confirmed by Dyson–Schwinger/Bethe–Salpeter equations in Yang–Mills theory. Particle accelerator experiments...
a kinetic term allowing for tunneling ("hopping") of particles between lattice sites and a potential term reflecting on-site interaction. The particles...
assigned to Hans Bethe's Theoretical (T) Division, and impressed Bethe enough to be made a group leader. He and Bethe developed the Bethe–Feynman formula...
the cation and anion gives the distance between the ions in a crystal lattice. Ionic radii are typically given in units of either picometers (pm) or...
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