XY model: Difference between revisions
Jump to navigation
Jump to search
mNo edit summary |
Carl McBride (talk | contribs) m (→See also: Added an internal link) |
||
| (6 intermediate revisions by the same user not shown) | |||
| Line 1: | Line 1: | ||
{{Stub-general}} | {{Stub-general}} | ||
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)== | |||
==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 14:15, 4 October 2016
|
This article is a 'stub' page, it has no, or next to no, content. It is here at the moment to help form part of the structure of SklogWiki. If you add sufficient material to this article then please remove the {{Stub-general}} template from this page. |
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)