Corrections to Universal Fluctuations in Correlated Systems: the 2D XY-model

Details Corrections to Universal Fluctuations in Correlated Systems: the 2D XY-model Corrections to Universal Fluctuations in Correlated Systems: the 2D XY-model

2005-06-28

arxiv.org/abs/cond-mat/0506713v1

Physics

Condensed Matter

Statistical Mechanics

To be published in Phys. Rev. E

Scientific paper

10.1103/PhysRevE.72.026119

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 2D 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).

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