Temperaturedependent fluctuations in the twodimensional XY model
Abstract
We present a detailed investigation of the probability density function (PDF) of order parameter fluctuations in the finite twodimensional XY (2dXY) model. In the lowtemperature critical phase of this model, the PDF approaches a universal nonGaussian limit distribution in the limit T → 0. Our analysis resolves the question of temperature dependence of the PDF in this regime, for which conflicting results have been reported. We show analytically that a weak temperature dependence results from the inclusion of multiple loop graphs in a previously derived graphical expansion. This is confirmed by numerical simulations on two controlled approximations to the 2dXY model: the harmonic and 'harmonic XY' models. The harmonic model has no KosterlitzThoulessBerezinskiĭ (KTB) transition and the PDF becomes progressively less skewed with increasing temperature until it closely approximates a Gaussian function above T ap 4π. Near to that temperature, we find some evidence of a phase transition, although our observations appear to exclude a thermodynamic singularity.
 Publication:

Journal of Physics A Mathematical General
 Pub Date:
 June 2005
 DOI:
 10.1088/03054470/38/25/001
 arXiv:
 arXiv:condmat/0507424
 Bibcode:
 2005JPhA...38.5603B
 Keywords:

 Statistical Mechanics
 EPrint:
 15 pages, 5 figures and 1 table