Exactly solvable models Exactly solvable models In dynamical systems theory, the baker's map is a chaotic map from the unit square into itself. It is topologically equivalent to the horseshoe map. In physics, a chain of coupled baker's maps can be used to model deterministic diffusion. The Poincaré recurrence time of the Baker's map is short compared to Hamiltonian maps. ...more on Wikipedia about "Baker's map"
In theoretical physics, an integrable model is a model, a theory or a set of equations whose exact solution may be calculated analytically in terms of elementary (or special) functions; the adjective integrable is therefore equivalent to "solvable". By a solution, one either means the exact partition function as a function of the parameters or the full set of correlation functions. Many models are integrable because of an enhanced symmetry, for example the conformal symmetry or supersymmetry. In the case of supersymmetry, the solution usually means the full low-energy effective action which includes the masses of BPS particles as functions of the moduli space. ...more on Wikipedia about "Integrable model"
The Ising model, named after the physicist Ernst Ising, is a mathematical model in statistical mechanics. It can be represented on a graph where its configuration space is the set of all possible assignments of +1 or -1 to each vertex of the graph. To complete the model, a function, E(e) must be defined, giving the difference between the energy of the "bond" associated with the edge when the spins on both ends of the bond are opposite and the energy when they are aligned. It's also possible to have an external magnetic field. ...more on Wikipedia about "Ising model"
The Korteweg-de Vries equation (KdV equation for short) is the following partial differential equation for a function φ of two real variables, x and t: ...more on Wikipedia about "Korteweg-de Vries equation"
The Kuramoto model, first proposed by Yoshiki Kuramoto (蔵本 由紀 Kuramoto Yoshiki), is a mathematical model for the behavior of a large set of coupled oscillators, and synchronization in general. Its formulation was motivated by the behavior of systems of chemical and biological oscillators, and it has found widespread applications. ...more on Wikipedia about "Kuramoto model"
In theoretical physics, the minimal models are a very concrete well-defined type of rational conformal field theory. The individual minimal models are parameterized by two integers p,q that are moreover related for the unitary minimal models. The first element of the sequence of the minimal models is the critical behavior of the Ising model, followed by the Potts model. There also exist supersymmetric minimal models. ...more on Wikipedia about "Minimal models"
In theoretical physics, the nonlinear Schrödinger equation is a nonlinear version of Schrödinger's equation in two dimensions. It can be considered as a classical equation, or a second quantized bosonic theory. It is an example of an integrable model. Its integrability is evidenced by the use of the inverse scattering transform, which takes the present equation and produces a linear system of equations, known as the Zakharov-Shabat system. ...more on Wikipedia about "Nonlinear Schrödinger equation"
In statistical mechanics, the Potts model, a generalization of the Ising model, is a model of interacting spins on a crystalline lattice. By studying the Potts model, one may gain insight into the behaviour of ferromagnets and certain other phenomena of solid state physics. The strength of the Potts model is not so much that it models these physical systems well; it is rather that the one-dimensional case is exactly solvable, and that it has a rich mathematical formulation that has been studied extensively. ...more on Wikipedia about "Potts model"
In physics, the Schwinger model, named after Julian Schwinger, is the model describing 2D Euclidean quantum electrodynamics with a Dirac fermion. This model exhibits a spontaneous symmetry breaking of the U(1) symmetry due to a chiral condensate due to a pool of instantons. The photon now becomes a massive particle. This model can be solved exactly and is used as a toy model for other more complex theories. ...more on Wikipedia about "Schwinger model"
The sine-Gordon equation is a partial differential equation in two dimensions. For a function of two real variables, x and t, it is ...more on Wikipedia about "Sine-Gordon equation"
In quantum field theory, the Thirring model is a model of a self-interacting Dirac field. In particular, if ψ is a Dirac spinor field, the Lagrangian density is given by ...more on Wikipedia about "Thirring model"
In the study of field theory and partial differential equations, a Toda field theory is derived from the following Lagrangian: ...more on Wikipedia about "Toda field theory"
In theoretical physics and mathematics, the Wess-Zumino-Witten (WZW) model, also called the Wess-Zumino-Novikov-Witten model, is a simple model of conformal field theory whose solutions are realized by affine Kac-Moody algebras. It is named after Julius Wess, Bruno Zumino, Sergei P. Novikov and Edward Witten. ...more on Wikipedia about "Wess-Zumino-Witten model"
The Yang-Baxter equation is an equation which was first introduced in the field of statistical mechanics. ...more on Wikipedia about "Yang-Baxter equation" shortopedia, just the best.
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