Lattice model

A statistical-mechanical model whose degrees of freedom occupy sites or links of a discrete lattice and interact according to specified rules.

Statistical mechanics: The study of macroscopic properties of matter through the statistics of microscopic states. Lattice models apply statistical mechanics to discrete arrangements of interacting variables.
Ising model: A lattice model with binary spins coupled through pairwise interactions. It is the canonical case where nearest-neighbor rules produce a magnetic phase transition.
Lattice QCD: A formulation of quantum chromodynamics on a discrete spacetime lattice. It uses lattice discretization to calculate strong-interaction physics nonperturbatively.
Continuum model: A model that represents space and fields as continuous rather than discrete. It replaces lattice sites and links with continuous degrees of freedom.
Lattice (group): A discrete subgroup of Euclidean space generated by linearly independent vectors. Periodic lattices provide the geometry on which many models place their variables.
Potts model: A lattice model whose sites take one of several discrete states and favor matching neighbors. It generalizes the Ising model's two local states to an arbitrary number.
Lattice gas automaton: A cellular model of fluid flow using particles that move and collide on a lattice. Its local rules reproduce macroscopic fluid behavior from discrete particle dynamics.
Mean-field theory: An approximation that replaces interactions with an average effective influence from the rest of a system. It suppresses spatial correlations that explicit lattice models can retain.
Lattice graph: A graph whose vertices and edges follow a regular, repeating spatial pattern. Its vertices and edges define sites, links, and neighborhood relations.
XY model: A lattice spin model with planar spins and interactions favoring alignment. Its continuous spin angles support topological behavior absent from binary-spin models.

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