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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 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.
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 ...
Barber–Layden–Power effect; Bare mass; Bargeboard (aerodynamics) ... Bethe ansatz; Bethe formula; Bethe lattice; Bethe–Bloch formula; Bethe–Feynman formula;
These are: the Barkas-Andersen-effect (proportional to z 3, after Walter H. Barkas and Hans Henrik Andersen), and the Felix Bloch-correction (proportional to z 4). In addition, one has to take into account that the atomic electrons of the material traversed are not stationary (" shell correction ").
the nature of the ligands surrounding the metal ion. The stronger the effect of the ligands then the greater the difference between the high and low energy d groups. The most common type of complex is octahedral, in which six ligands form the vertices of an octahedron around the metal ion.
In 1947, Hans Bethe was the first to explain the Lamb shift in the hydrogen spectrum, and he thus laid the foundation for the modern development of quantum electrodynamics. Bethe was able to derive the Lamb shift by implementing the idea of mass renormalization, which allowed him to calculate the observed energy shift as the difference between ...