Heisenberg model (quantum) exhibits quasi-long range order. Heisenberg model (quantum) The Heisenberg model is a statistical mechanical model used in the study of critical points and phase transitions of magnetic systems, in which the spins of the magnetic systems are treated quantum mechanically. In the prototypical Ising model, defined on a "d"-dimensional lattice, at each lattice site, a spin formula_1 represents a microscopic magnetic dipole to which the magnetic moment is either up or down. Except the coupling between magnetic dipole moments, there is also a multipolar version of Heisenberg model called the multipolar exchange interaction. For quantum mechanical reasons (see exchange interaction
Heisenberg group given action of the central Lie algebra element "z", up to a unitary equivalence: the nontrivial elements of the algebra are all equivalent to the usual position and momentum operators. Thus, the Schrödinger picture and Heisenberg picture are equivalent – they are just different ways of realizing this essentially unique representation. The same uniqueness result was used by David Mumford for discrete Heisenberg groups, in his theory of equations defining abelian varieties. This is a large generalization of the approach used in Jacobi's elliptic functions, which is the case of the modulo 2 Heisenberg group, of order 8. The simplest