- Lattice model (physics)
:"For other meanings, see

lattice model (disambiguation) "Inphysics , a**lattice model**is aphysical model that is defined on a lattice, as opposed to thecontinuum ofspace orspacetime . Lattice models originally occurred in the context ofcondensed matter physics , where theatom s of acrystal automatically form a lattice. Currently, lattice models are quite popular intheoretical physics , for many reasons. Some models areexactly solvable , and thus offer insight into physics beyond what can be learned fromperturbation theory . Lattice models are also ideal for study by the methods ofcomputational physics , as the discretization of any continuum model automatically turns it into a lattice model.Examples of lattice models in

condensed matter physics include theIsing model , thePotts model , theXY model , theToda lattice . The exact solution to many of these models (when they are solvable) includes the presence ofsoliton s. Techniques for solving these include theinverse scattering transform and the method ofLax pair s, theYang-Baxter equation andquantum group s. The solution of these models has given insights into the nature ofphase transitions ,magnetization andscaling behaviour , as well as insights into the nature ofquantum field theory .Lattice models frequently occur as an approximation to a continuum theory, either to give an

ultraviolet cutoff to the theory to prevent divergences or to perform numerical computations. An example of a continuum theory that is widely studied by lattice models is theQCD lattice model , a discretization ofquantum chromodynamics . More generally,lattice gauge theory andlattice field theory are areas of study.**ee also***

Scaling limit

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