XY model: Difference between revisions
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*[[RP(n-1) model]] | *[[RP(n-1) model]] | ||
==References== | ==References== | ||
<references/> | |||
;Related reading | |||
*[http://dx.doi.org/10.1140/epjb/e2006-00172-3 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)] | |||
*[http://dx.doi.org/10.1063/1.4830400 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)] | |||
[[category: models]] | [[category: models]] | ||
Revision as of 17:04, 28 February 2014
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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 (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}\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.
Random field XY model (RFXY)
XY universality class
- (see: XY universality class)
See also
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)