Lattice models
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 p...
Lattice models - Wikipedia
Bose–Hubbard model
The Bose–Hubbard model gives an approximate description of the physics of interacting bosons on a lattice. It is closely related to the Hubbard model which originated in solid-state physics as ...
Cayley graph
In mathematics, a Cayley graph, also known as a Cayley colour graph, Cayley diagram, group diagram, or colour group is a graph that encodes the abstract structure of a group. Its definition is suggest...
Cayley graph - Wikipedia
Antiferromagnetism
In materials that exhibit antiferromagnetism, the magnetic moments of atoms or molecules, usuallyrelated to the spins of electrons, align in a regular pattern with neighboring spins (on different subl...
Antiferromagnetism - Wikipedia
Spherical model
The spherical model in statistical mechanics is a model of ferromagnetism similar to the Ising model, which was solved in 1952 by T. H. Berlin and M. Kac. It has the remarkable property that when appl...
Cellular Potts model
The cellular Potts model is a lattice-based computational modeling method to simulate the collective behavior of cellular structures. Other names for the CPM are extended large-q Potts model and Glaz...
Cellular Potts model - Wikipedia
Stochastic cellular automaton
Stochastic cellular automata or 'probabilistic cellular automata' (PCA) or 'random cellular automata' or locally interacting Markov chains are an important extension of cellular automaton. Cellular au...
Hamiltonian lattice gauge theory
In physics, Hamiltonian lattice gauge theory is a calculational approach to gauge theory and a special case of lattice gauge theory in which the space is discretized but time is not. The Hamiltonian i...
Quasi-harmonic approximation
The quasi-harmonic approximation is a phonon-based model of solid-state physics used to describe volume-dependent thermal effects, such as the thermal expansion. It is based on the assumption that the...
Domino tiling
A domino tiling of a region in the Euclidean plane is a tessellation of the region by dominos, shapes formed by the union of two unit squares meeting edge-to-edge. Equivalently, it is a matching in th...
Domino tiling - Wikipedia
Lattice density functional theory
Lattice density functional theory (LDFT) is a statistical theory used in physics and thermodynamics to model a variety of physical phenomena with simple lattice equations. Lattice models with nearest-...
Fermion doubling
The fermion doubling problem is a problem that is encountered when naively trying to put fermionic fields on a lattice. It consists in the appearance of spurious states, such that one ends up having 2...
Quantum dimer models
Quantum dimer models were introduced to model the physics of resonating valence bond (RVB) states in lattice spin systems. The only degrees of freedom retained from the motivating spin systems are t...
Lattice Boltzmann methods
Lattice Boltzmann methods (LBM) (or Thermal Lattice Boltzmann methods (TLBM)) is a class of computational fluid dynamics (CFD) methods for fluid simulation. Instead of solving the Navier–Stokes equati...
Percolation theory
In mathematics, percolation theory describes the behavior of connected clusters in a random graph. The applications of percolation theory to materials science and other domains are discussed in the ar...
Percolation theory - Wikipedia
Ising model
The Ising model (/ˈaɪsɪŋ/; [ˈiːzɪŋ]), named after the physicist Ernst Ising, is a mathematical model of ferromagnetism in statistical mechanics. The model consists of discrete variables that represent...
Ising model - Wikipedia
Corner transfer matrix
In statistical mechanics, the corner transfer matrix describes the effect of adding a quadrant to a lattice. Introduced by Rodney Baxter in 1968 as an extension of the Kramers-Wannier row-to-row trans...
Corner transfer matrix - Wikipedia
Kramers–Wannier duality
The Kramers–Wannier duality is a symmetry in statistical physics. It relates the free energy of a two-dimensional square-lattice Ising model at a low temperature to that of another Ising model at a h...
Voter model
In the mathematical theory of probability, the voter model is a stochastic process that is a specific type of interacting particle system (see Probabilistic Cellular Automata too). A voter model is a ...
Voter model - Wikipedia
N-vector model
The n-vector model or O(n) model has been introduced by H. Eugene Stanley is one of the many highly simplified models in the branch of physics known as statistical mechanics. In the n-vector model,...
Z N model
The model is a simplified statistical mechanical spin model. It is a generalization of the Ising model. Although it can be defined on an arbitrary graph, it is integrable only on one and two-dimensi...
Ice-type model
In statistical mechanics, the ice-type models or six-vertex models are a family of vertex models for crystal lattices with hydrogen bonds. The first such model was introduced by Linus Pauling in 1935 ...
Ice-type model - Wikipedia
Feynman checkerboard
The Feynman Checkerboard or Relativistic Chessboard model was Richard Feynman’s sum-over-paths formulation of the kernel for a free spin ½ particle moving in one spatial dimension. It provides a rep...
Feynman checkerboard - Wikipedia
Square-lattice Ising model
In statistical mechanics, the two-dimensional square-lattice Ising model is a simple model of interacting magnetic spins. The model is notable for having nontrivial interactions, yet having an analyti...
Square-lattice Ising model - Wikipedia
Graphene
Graphene (/ˈɡræf.iːn/) is an allotrope of carbon in the form of a two-dimensional, atomic-scale, hexagonal lattice in which one atom forms each vertex. It is the basic structural element of other allo...
Graphene - Wikipedia
Lattice model (physics)
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 p...
Lattice model (physics) - Wikipedia
AKLT Model
The AKLT model is an extension of the one-dimensional quantum Heisenberg spin model. The proposal and exact solution of this model by Affleck, Lieb, Kennedy and Tasaki provided crucial insight into th...
AKLT Model - Wikipedia
Tetron Model
The Tetron Model was developed by Bodo Lampe in an attempt to reduce the 24 observed quark and lepton flavors and their interactions to a simple structure based on the permutation group S4, according ...
Tetron Model - Wikipedia
Classical Heisenberg model
The Classical Heisenberg model is the case of the n-vector model, one of the models used in statistical physics to model ferromagnetism, and other phenomena.
It can be formulated as follows: take...