Correlation functions for the $XY$ model in a Magnetic Field
| dc.creator | Zhang, Wei | |
| dc.creator | Fertig, H. A. | |
| dc.date | 2006-03-01 | |
| dc.date.accessioned | 2026-07-07T07:02:03Z | |
| dc.date.available | 2026-07-07T07:02:03Z | |
| dc.description | Recent studies of the two-dimensional, classical $XY$ magnet in a magnetic field suggest that it has three distinct vortex phases: a linearly confined phase, a logarithmically confined phase, and a free vortex phase. In this work we study spin-spin correlation functions in this model by analytical analysis and numerical simulations to search for signatures of the various phases. In all three phases, the order parameter is nonzero and $<\cos(þ({\bf r}_1))\cos(þ({\bf r}_2))>$ remains nonzero for $r \equiv |{\bf r}_1-{\bf r}_2|\rightarrow \infty$, indicating the expected long range order. The correlation function for transverse fluctuations of the spins, $C(r)=<\sin(þ({\bf r}_1))\sin(þ({\bf r}_2))>$, falls exponentially in all three phases. A renormalization group analysis suggests that the logarithmically confined phase should have a spatially anisotropic correlation length. In addition, there is a generic anisotropy in the prefactor which is always present. We find that this prefactor anisotropy becomes rather strong in the presence of a magnetic field, masking the effects of any anisotropy in the correlation length in the simulations. | |
| dc.description | 17 pages, 5 figures | |
| dc.identifier | https://arxiv.org/abs/cond-mat/0603028 | |
| dc.identifier | http://arxiv.org/abs/cond-mat/0603028 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/108471 | |
| dc.subject | Other Condensed Matter | |
| dc.title | Correlation functions for the $XY$ model in a Magnetic Field | |
| dc.type | text |