Classical XY model

The XY model is a generalization of the Ising model of statistical mechanics, with the magnetism and other physical phenomena can be described.

It consists of N by unit vectors spins shown disposed on the points of a lattice of any dimension, but can be oriented only in one plane. The Hamiltonian for the XY model is given by

Being summed over the nearest neighbor spins, " " the standard scalar product of the two-dimensional Euclidean space and an external magnetic field is. The order parameter of the XY model is the magnetization and thus a vector. A phase transition can occur for two - and higher-dimensional lattice. In two dimensions, this is not a normal continuous phase transition or phase transition of first order, but the writable by any conventional local order parameter Kosterlitz - Thouless transition. This transition is the main reason why the XY model for theoretical physics is interesting.

XY model is a special case of n = 2 of the more general n-vector model.