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The Ising model is a mathematical model of ferromagnetism, in which the magnetic properties of a material are represented by a "spin" at each node in the lattice, which is either +1 or -1. The model is also equipped with a constant K {\displaystyle K} representing the strength of the interaction between adjacent nodes, and a constant h ...
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.
One problem in the theory of Gaudin models is then to determine when a given configuration is complete or not, or at least characterize the 'space of models' for which the Bethe ansatz is complete. For g = s l 2 {\displaystyle {\mathfrak {g}}={\mathfrak {sl}}_{2}} , for z i {\displaystyle z_{i}} in general position the Bethe ansatz is known to ...
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 ...
A simplified illustration of the spin chain model. The spin of the ith site can interact with the spins from the i - 1 and i + 1 sites. A spin chain is a type of model in statistical physics. Spin chains were originally formulated to model magnetic systems, which typically consist of particles with magnetic spin located at fixed sites on a lattice.
Jennifer "Jen" Marie Schwarz is an American physicist whose research applies ideas from condensed matter physics including percolation theory, jamming, dislocation avalanches, and rigidity transitions to biological structures and quantum systems. She is a professor of physics at Syracuse University. [1]
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.
The hunt for solvable lattice models has been actively pursued since then, culminating in Baxter's solution of the eight vertex model [5] in 1972. Another line of development was the theory of factorized S-matrix in two dimensional quantum field theory. [ 6 ]