 Classical Heisenberg model

The Classical Heisenberg model is the n = 3 case of the nvector model, one of the models used in statistical physics to model ferromagnetism, and other phenomena.
Contents
Definition
It can be formulated as follows: take a ddimensional lattice, and a set of spins of the unit length
 ,
each one placed on a lattice node.
The model is defined through the following Hamiltonian:
with
a coupling between spins.
Properties
 Polyakov has conjectured that, in dimension 2, as opposed to the classical XY model, there is no dipole phase for any T > 0; i.e. at nonzero temperature the correlations cluster exponentially fast.^{[1]}
 The general mathematical formalism used to describe and solve the Heisenberg model and certain generalizations is developed in the article on the Potts model.
 In the continuum limit the Heisenberg model (2) gives the following equation of motion

 This equation is called the continuous classical Heisenberg ferromagnet equation or shortly Heisenberg model and is integrable in the soliton sense. It admits several integrable and nonintegrable generalizations like LandauLifshitz equation, Ishimori equation and so on.
See also
 Heisenberg model (quantum)
 Ising model
 Classical XY model
 Magnetism
 Ferromagnetism
 LandauLifshitz equation
 Ishimori equation
References
 ^ Polyakov, A.M. (1975). Phys.Letts. B 59. Bibcode 1975PhLB...59...79P. doi:10.1016/03702693(75)901616. http://www.sciencedirect.com/science/article/pii/0370269375901616.
External links
 Absence of Ferromagnetism or Antiferromagnetism in One or TwoDimensional Isotropic Heisenberg Models
 The Heisenberg Model  a Bibliography
Categories: Magnetic ordering
 Spin models
 Condensed matter physics
 Lattice models
 Physics stubs
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