Mermin–Wagner theorem

The Mermin -Wagner theorem, named after N. David Mermin and Herbert Wagner, is a theorem of theoretical physics of magnetism and states that there can be in one - and two-dimensional systems at temperatures above absolute zero no ferromagnetism or antiferromagnetism, as long as these are isotropic. This follows from a theoretical calculation in the Heisenberg model or rather the derived Ising model in one dimension and the XY model in two dimensions. It follows that, assuming isotropy of the system can occur no phase transition of second order. Therefore can not pass from the paramagnetic phase to the ferromagnetic or antiferromagnetic phase such a system.

In reality, the anisotropy of the system but is already achieved at existing LS- coupling.

As a result of the work of Mermin and Wagner has been similarly demonstrated that it also can be no superconductivity and no long-range crystalline order in isotropic interaction in one- and two-dimensional. Here, too (eg in the graphene ) but are violated the conditions of the theorem in practice in several ways.