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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.
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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 .
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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".
"(Note that the Bethe lattice is actually an unrooted tree, since any vertex will serve equally well as a root.) " Although it is true that any vertex will serve equally as a root, that is not the reason that the Bethe lattice is an unrooted tree. The reason that it is an unrooted tree is that it is defined to be an unrooted tree.
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.
Lattice constants of atomic crystals are of the order of 1Å while those of superlattices (a) are several hundreds or thousands larger as dictated by technological limits (e.g. electron-beam lithography used for the patterning of the heterostructure surface). Energies are correspondingly smaller in superlattices.