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The '''XY model''', also known as the ''O(2)'' model, is a Heisenberg ferromagnetic with an easy-plane anisotropy. | 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 | ||
:<math>H = -J{\sum}_{\langle i,j\rangle}\mathbf{S}_i \cdot \mathbf{S}_{j}</math> | |||
in other words | |||
:<math>H=-J{\sum}_{\langle i,j\rangle}\cos(\theta_i-\theta_j)</math> | |||
where the sum runs over all pairs of nearest neighbour spins, <math>\mathbf{S}</math>, and where <math>J</math> is the coupling constant. | |||
==Random field XY model (RFXY)== | ==Random field XY model (RFXY)== | ||
==XY universality class== | |||
:(''see: [[Universality classes#XY | XY universality class]]'') | |||
==See also== | ==See also== | ||
*[[Heisenberg model]] | *[[Heisenberg model]] | ||
*[[Kosterlitz-Thouless transition]] | |||
*[[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)] | |||
*[http://dx.doi.org/10.1063/1.4880417 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)] | |||
[[category: models]] | [[category: models]] | ||
Latest revision as of 13:15, 4 October 2016
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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
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)