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| {{Stub-general}} | | {{Stub-general}} |
| 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 | | The '''XY model''', also known as the ''O(2)'' model, is a Heisenberg ferromagnetic with an easy-plane anisotropy. |
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| :<math>H = -J{\sum}_{\langle i,j\rangle}\mathbf{S}_i \cdot \mathbf{S}_{j}</math>
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| in other words
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| :<math>H=-J{\sum}_{\langle i,j\rangle}\cos(\theta_i-\theta_j)</math>
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| where the sum runs over all pairs of nearest neighbour spins, <math>\mathbf{S}</math>, and where <math>J</math> is the coupling constant.
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| ==Random field XY model (RFXY)== | | ==Random field XY model (RFXY)== |
| ==XY universality class== | | ==XY universality class== |
| :(''see: [[Universality classes#XY | XY universality class]]'')
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| ==See also== | | ==See also== |
| *[[Heisenberg model]] | | *[[Heisenberg model]] |
| *[[Kosterlitz-Thouless transition]]
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| *[[RP(n-1) model]] | | *[[RP(n-1) model]] |
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| ==References== | | ==References== |
| <references/>
| | #[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)] |
| ;Related reading
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| *[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)]
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| *[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)]
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| *[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)]
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| [[category: models]] | | [[category: models]] |