Physics – Condensed Matter – Other Condensed Matter
Scientific paper
2006-03-01
Physics
Condensed Matter
Other Condensed Matter
17 pages, 5 figures
Scientific paper
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 $<\cos(\th({\bf r}_1))\cos(\th({\bf r}_2))>$ 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, $C(r)=<\sin(\th({\bf r}_1))\sin(\th({\bf r}_2))>$, 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.
Fertig Herbert A.
Zhang Wanchuan
No associations
LandOfFree
Correlation functions for the $XY$ model in a Magnetic Field does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Correlation functions for the $XY$ model in a Magnetic Field, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Correlation functions for the $XY$ model in a Magnetic Field will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-368767