Temperature dependent fluctuations in the two-dimensional XY model

Abstract

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 ~ 4π. Near to that temperature we find some evidence of a phase transition, although our observations appear to exclude a thermodynamic singularity.

15 pages, 5 figures and 1 table

References in corpus (16)

• Universal Fluctuations in Correlated Systems
• 1/f Noise and Extreme Value Statistics
• Magnetic fluctuations in the classical XY model: the origin of an exponential tail in a complex system
• Out-of-equilibrium dynamical fluctuations in glassy systems
• Fluctuation and Dissipation in Liquid Crystal Electroconvection
• Universal features of the order-parameter fluctuations : reversible and irreversible aggregation
• Universal Fluctuations of the Danube Water Level: a Link with Turbulence, Criticality and Company Growth
• Universal fluctuations and extreme value statistics
• Criterion for universality class independent critical fluctuations: example of the 2D Ising model
• Extremum statistics: A framework for data analysis
• Distribution of injected power fluctuations in electroconvection
• Non-Gaussian Resistance Noise near Electrical Breakdown in Granular Materials
• Statistical properties of one dimensional "turbulence"
• Non-Gaussianity of resistance fluctuations near electrical breakdown
• Finite size scaling in the 2D XY-model and generalized universality
• Vortex corrections to universal scaling of magnetic fluctuations in 2D XY model

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