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

$H=-J{\sum }_{\langle i,j\rangle }\mathbf {S} _{i}\cdot \mathbf {S} _{j}$

in other words

$H=-J{\sum }_{\langle i,j\rangle }\cos(\theta _{i}-\theta _{j})$

where the sum runs over all pairs of nearest neighbour spins, Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \mathbf{S}} , and where Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle J} is the coupling constant.

XY universality class

(see: XY universality class)

See also

• Heisenberg model
• RP(n-1) model

References

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)