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 real Lie group of dimension 3. In addition to the representation as real 3x3 matrices, the continuous Heisenberg group also has several different representations in terms of function spaces. By Stone–von Neumann theorem, there is, up to isomorphism, a unique irreducible unitary representation of H in which its centre acts by a given nontrivial character. This representation has several important realizations, or models. In the "Schrödinger model", the Heisenberg group acts on the space of square integrable functions. In the theta representation, it acts on the space of holomorphic functions on the upper half-plane; it is so named for its