Origin of the approximate universality of distributions in equilibrium correlated systems

Abstract

We propose an interpretation of previous experimental and numerical experiments, showing that for a large class of systems, distributions of global quantities are similar to a distribution originally obtained for the magnetization in the 2D-XY model . This approach, developed for the Ising model, is based on previous numerical observations. We obtain an effective action using a perturbative method, which successfully describes the order parameter fluctuations near the phase transition. This leads to a direct link between the D-dimensional Ising model and the XY model in the same dimension, which appears to be a generic feature of many equilibrium critical systems and which is at the heart of the above observations.

arXiv commentTo appear in Europhysics Letters

References in corpus (13)

• 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
• Roughness distributions for 1/f^alpha signals
• Universal interface width distributions at the depinning threshold
• Statistical Mechanics of Kinks in (1+1)-Dimensions: Numerical Simulations and Double Gaussian Approximation
• Criterion for universality class independent critical fluctuations: example of the 2D Ising model
• Universal Magnetic Fluctuations with a Field Induced Length Scale
• Distribution of injected power fluctuations in electroconvection
• Finite size scaling in the 2D XY-model and generalized universality
• Temperature dependent fluctuations in the two-dimensional XY model
• Corrections to Universal Fluctuations in Correlated Systems: the 2D XY-model

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• Cluster Algorithm Renormalization Group Study of Universal Fluctuations in the 2D Ising Model
• Dissipation induced non-Gaussian energy fluctuations
• Nature of the global fluctuations in the spherical model at criticality