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Lattice model

In physics, a lattice model is a physical model that is not defined on a continuum, but on a lattice, which is a graph or an n-complex approximating spacetime or space. The lattice is translationally invariant if it is generated by a subgroup of translationss acting upon a finite number of points. Of course, any arbitrary triangulation would do as well.

In condensed matter physics, the atoms of a crystal automatically form a lattice and this is one application of lattice theory.

See Ising model, XY model

Another is as an approximation to a continuum theory, either to give an ultraviolet cutoff to the theory to prevent divergences or to perform numerical computations.

See QCD lattice models

As an aside, everytime someone does numerical computations for partial differential equations, they are really dealing with a lattice theory because computers only work with discrete data.

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