- Lattice model (physics)
:"For other meanings, see
lattice model (disambiguation)"In physics, a lattice model is a physical modelthat is defined on a lattice, as opposed to the continuumof spaceor spacetime. Lattice models originally occurred in the context of condensed matter physics, where the atoms of a crystalautomatically form a lattice. Currently, lattice models are quite popular in theoretical physics, for many reasons. Some models are exactly solvable, and thus offer insight into physics beyond what can be learned from perturbation theory. Lattice models are also ideal for study by the methods of computational physics, as the discretization of any continuum model automatically turns it into a lattice model.
Examples of lattice models in
condensed matter physicsinclude the Ising model, the Potts model, the XY model, the Toda lattice. The exact solution to many of these models (when they are solvable) includes the presence of solitons. Techniques for solving these include the inverse scattering transformand the method of Lax pairs, the Yang-Baxter equationand quantum groups. The solution of these models has given insights into the nature of phase transitions, magnetizationand scaling behaviour, as well as insights into the nature of quantum field theory.
Lattice models frequently occur as an approximation to a continuum theory, either to give an
ultraviolet cutoffto the theory to prevent divergences or to perform numerical computations. An example of a continuum theory that is widely studied by lattice models is the QCD lattice model, a discretization of quantum chromodynamics. More generally, lattice gauge theoryand lattice field theoryare areas of study.
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