2006/03/01 by Zhang, Wei, Fertig, H. A.
#FOS: Physical sciences #Other Condensed Matter (cond-mat.other)
paper · doi:10.48550/arxiv.cond-mat/0603028
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 remains nonzero for r ≡ |\bf r1-\bf r2|→ ∞, indicating the expected long range order. The correlation function for transverse fluctuations of the spins, C(r)=, 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.