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

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

in other words

Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle 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)
• 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)