Physics – Condensed Matter – Statistical Mechanics
Scientific paper
2005-07-18
J. Phys. A: Math. Gen. 38, 5603 (2005)
Physics
Condensed Matter
Statistical Mechanics
15 pages, 5 figures and 1 table
Scientific paper
10.1088/0305-4470/38/25/001
We present a detailed investigation of the probability density function (PDF) of order parameter fluctuations in the finite two-dimensional XY (2dXY) model. In the low temperature critical phase of this model, the PDF approaches a universal non-Gaussian 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 Kosterlitz-Thouless-Berezinskii (KTB) transition and the PDF becomes progressively less skewed with increasing temperature until it closely approximates a Gaussian function above T ~ 4\pi. Near to that temperature we find some evidence of a phase transition, although our observations appear to exclude a thermodynamic singularity.
Banks T. S.
Bramwell Steven. T.
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