# XY model

The **XY model**, also known as the *O(2)* model because of its symmetry group, is a Heisenberg ferromagnetic with an easy-plane anisotropy. The Hamiltonian is given by

in other words

where the sum runs over all pairs of nearest neighbour spins, , and where is the coupling constant.

## Random field XY model (RFXY)[edit]

## XY universality class[edit]

- (
*see: XY universality class*)

## See also[edit]

## References[edit]

- Related reading

- L.A.S. Mól, A.R. Pereira, H. Chamati and S. Romano "Monte Carlo study of 2D generalized XY-models", European Physical Journal B
**50**pp. 541-548 (2006) - Dhagash Mehta, Ciaran Hughes, Mario Schröck and David J. Wales "Potential energy landscapes for the 2D XY model: Minima, transition states, and pathways", Journal of Chemical Physics
**139**194503 (2013) - D. Mehta, C. Hughes, M. Kastner and D. J. Wales "Potential energy landscape of the two-dimensional XY model: Higher-index stationary points", Journal of Chemical Physics
**140**224503 (2014)