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 model (quantum) respectively. Other approaches do so without Bethe ansatz. The physics of the Heisenberg model strongly depends on the sign of the coupling constant formula_3 and the dimension of the space. For positive formula_3 the ground state is always ferromagnetic. At negative formula_3 the ground state is antiferromagnetic in two and three dimensions, it is from this ground state that the Hubbard model is given. In one dimension the nature of correlations in the antiferromagnetic Heisenberg model depends on the spin of the magnetic dipoles. If the spin is integer then only short-range order is present. A system of half-integer spins