Corrections to universal fluctuations in correlated systems: the two-dimensional XY model.
Generalized universality, as recently proposed, postulates a universal non-Gaussian form of the probability density function (PDF) of certain global observables for a wide class of highly correlated systems of finite volume N. Studying the two-dimensional XY model, we link its validity to renormalization group properties. It would be valid if there were a single dimension 0 operator, but the actual existence of several such operators leads to T-dependent corrections. The PDF is the Fourier transform of the partition function Z(q) of an auxiliary theory which differs by a dimension 0 perturbation with a very small imaginary coefficient iq/N from a theory which is asymptotically free in the infrared. We compute the PDF from a systematic loop expansion of ln Z(q).
Mack
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II. Institut für Theoretische Physik, Universität Hamburg, D-22761 Hamburg, Luruper Chaussee 149, Germany. gerhard.mack@desy.de
Palma
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Vergara
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