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

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).

arXiv commentTo be published in Phys. Rev. E

References in corpus (5)

• Universal Fluctuations in Correlated Systems
• A ``Tetris''-like model for the Compaction of Dry Granular Media
• Magnetic fluctuations in the classical XY model: the origin of an exponential tail in a complex system
• Fluctuations in finite critical and turbulent systems
• Finite size scaling in the 2D XY-model and generalized universality

Cited by in corpus (6)

• Global fluctuations in physical systems: a subtle interplay between sum and extreme value statistics
• Constraint Effective Potential of the Magnetization in the Quantum XY Model
• Origin of the approximate universality of distributions in equilibrium correlated systems
• Finite-size corrections to scaling of the magnetization distribution in the $2d$ $XY$-model at zero temperature
• Cluster Algorithm Renormalization Group Study of Universal Fluctuations in the 2D Ising Model
• Extreme statistics, Gaussian statistics, and superdiffusion in global magnitude fluctuations in turbulence