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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