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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.
In statistical mechanics, bootstrap percolation is a percolation process in which a random initial configuration of active cells is selected from a lattice or other space, and then cells with few active neighbors are successively removed from the active set until the system stabilizes. The order in which this removal occurs makes no difference ...
In his article "Restructuring Lattice Theory" (1982), [1] initiating formal concept analysis as a mathematical discipline, Wille starts from a discontent with the current lattice theory and pure mathematics in general: The production of theoretical results—often achieved by "elaborate mental gymnastics"—were impressive, but the connections between neighboring domains, even parts of a ...
Carlson was appointed to the faculty at the University of California, Santa Barbara in 1990. She works on the fundamental theory and applications of complex systems. [4] [5] She was awarded a David and Lucile Packard Foundation fellowship in 1993, which allowed her to study the physical and mathematical principles that underlie complexity. [6]
In mathematics, a supermodular function is a function on a lattice that, informally, has the property of being characterized by "increasing differences." Seen from the point of set functions, this can also be viewed as a relationship of "increasing returns", where adding more elements to a subset increases its valuation.
A partially ordered set that is both a join-semilattice and a meet-semilattice is a lattice. A lattice in which every subset, not just every pair, possesses a meet and a join is a complete lattice. It is also possible to define a partial lattice, in which not all pairs have a meet or join but the operations (when defined) satisfy certain axioms ...
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