Ad
related to: bethe lattice theory
Search results
Results From The WOW.Com Content Network
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 regular tree where all vertices have the same number of neighbors. The Bethe lattice was introduced into the physics literature by Hans Bethe in 1935.
The idea first appeared in physics (statistical mechanics) in the work of Pierre Curie [6] and Pierre Weiss to describe phase transitions. [7]MFT has been used in the Bragg–Williams approximation, models on Bethe lattice, Landau theory, Curie-Weiss law for magnetic susceptibility, Flory–Huggins solution theory, and Scheutjens–Fleer theory.
In physics, the Bethe ansatz is an ansatz for finding the exact wavefunctions of certain quantum many-body models, most commonly for one-dimensional lattice models.It was first used by Hans Bethe in 1931 to find the exact eigenvalues and eigenvectors of the one-dimensional antiferromagnetic isotropic (XXX) Heisenberg model.
For site percolation on the square lattice, the value of p c is not known from analytic derivation but only via simulations of large lattices which provide the estimate p c = 0.59274621 ± 0.00000013. [7] A limit case for lattices in high dimensions is given by the Bethe lattice, whose threshold is at p c = 1 / z − 1 for a ...
Limits of the model as the lattice spacing is sent to zero (and various limits are taken for variables appearing in the theory) describes integrable field theories, both non-relativistic such as the nonlinear Schrödinger equation, and relativistic, such as the sigma model, the sigma model (which is also a principal chiral model) and the sine ...
Dynamical mean-field theory, a non-perturbative treatment of local interactions between electrons, bridges the gap between the nearly free electron gas limit and the atomic limit of condensed-matter physics. [1] DMFT consists in mapping a many-body lattice problem to a many-body local problem, called an impurity model. [2]
It can be regarded as a generalization of the Bethe–Peierls iterative method in tree-like graphs, to the case of a graph with loops that are not too short. The cavity method can solve many problems also solvable using the replica trick but has the advantage of being more intuitive and less mathematically subtle than replica-based methods.
In quantum physics, the quantum inverse scattering method (QISM), similar to the closely related algebraic Bethe ansatz, is a method for solving integrable models in 1+1 dimensions, introduced by Leon Takhtajan and L. D. Faddeev in 1979.
Ad
related to: bethe lattice theory