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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.
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 .
The DMFT treatment of lattice quantum models is similar to the mean-field theory (MFT) treatment of classical models such as the Ising model. [6] In the Ising model, the lattice problem is mapped onto an effective single site problem, whose magnetization is to reproduce the lattice magnetization through an effective "mean-field".
A normal subgroup has been known since the 1940s to be left and (dual) right modular as an element of the lattice of subgroups. [1] Richard Stanley noticed in the 1970s that certain geometric lattices, such as the partition lattice, obeyed similar properties, and gave a lattice-theoretic abstraction. [2] [3]
The Bethe–Slater curve is a heuristic explanation for why certain metals are ferromagnetic and others are antiferromagnetic. It assumes a Heisenberg model of magnetism, and explains the differences in exchange energy of transition metals as due to the ratio of the interatomic distance a to the radius r of the 3d electron shell . [ 1 ]
I'm not an expert in the field, but I happened to read a related article (Pys.Rev.E 75(2007)026105 on the Ising model on networks with Cayley-tree-like structure. In it, it was mentioned the difference of behaviors when the model is applied on a Cayley tree, vs. the model applied on a Bethe lattice.
Denneno's Pizza in Stoughton is closing this December after 69 years in business. Barstool Sports founder Dave Portnoy made sure to review it first.
In mathematical physics, a lattice model is a mathematical model of a physical system that is defined on a lattice, as opposed to a continuum, such as the continuum of space or spacetime. Lattice models originally occurred in the context of condensed matter physics, where the atoms of a crystal automatically form a lattice.