Warning: You are not logged in. Your IP address will be publicly visible if you make any edits. If you
log in or
create an account, your edits will be attributed to your username, along with other benefits.
The edit can be undone.
Please check the comparison below to verify that this is what you want to do, and then publish the changes below to finish undoing the edit.
Latest revision |
Your text |
Line 1: |
Line 1: |
| {{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
| |
|
| |
| :<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]]
| |
| *[[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]] |