In physics, a lattice model is a physical
model that is defined on a lattice, as opposed
to the continuum of space or spacetime.
Lattice models originally occurred in the
context of condensed matter physics, where
the atoms of a crystal automatically 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
physics include 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 transform and the method of Lax
pairs, the Yang-Baxter equation and quantum
groups.
The solution of these models has given insights
into the nature of phase transitions, magnetization
and scaling behaviour, as well as insights
into the nature of quantum field theory.
Physical 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 the QCD lattice
model, a discretization of quantum chromodynamics.
However, digital physics considers nature
fundamentally discrete at the Planck scale,
which imposes upper limit to the density of
information, aka Holographic principle.
More generally, lattice gauge theory and lattice
field theory are areas of study.
Lattice models are also used to simulate the
structure and dynamics of polymers.
Examples include the bond fluctuation model
and the 2nd model.
== See also ==
Crystal structure
Lattice gauge theory
Lattice QCD
Scaling limit
QCD matter
Lattice gas
