![]() ![]() ![]() Lattice models are also used to simulate the structure and dynamics of polymers.Ī number of lattice models can be described by the following data: More generally, lattice gauge theory and lattice field theory are areas of study. However, digital physics considers nature fundamentally discrete at the Planck scale, which imposes upper limit to the density of information, aka Holographic principle. An example of a continuum theory that is widely studied by lattice models is the QCD lattice model, a discretization of quantum chromodynamics. 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. 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. Techniques for solving these include the inverse scattering transform and the method of Lax pairs, the Yang–Baxter equation and quantum groups. The exact solution to many of these models (when they are solvable) includes the presence of solitons. 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. Some models are exactly solvable, and thus offer insight into physics beyond what can be learned from perturbation theory. Currently, lattice models are quite popular in theoretical physics, for many reasons. Lattice models originally occurred in the context of condensed matter physics, where the atoms of a crystal automatically form a lattice. In mathematical physics, a lattice model is a mathematical model of a physical system that is defined on a lattice, as opposed to a continuum, such as the continuum of space or spacetime. Lattices such as this are used - for example - in the Flory–Huggins solution theory A three-dimensional lattice filled with two molecules A and B, here shown as black and white spheres. For other uses, see Lattice model (disambiguation). ![]()
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