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

TL;DR

This paper investigates the universality of probability density functions in the 2D XY-model, revealing how multiple operators cause temperature-dependent corrections to the expected universal form.

Contribution

It links the validity of generalized universality to renormalization group properties and computes the PDF using a systematic loop expansion, highlighting the role of multiple operators.

Findings

Multiple operators lead to T-dependent corrections.

PDF derived from partition function of an auxiliary theory.

Systematic loop expansion used for PDF calculation.

Abstract

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).