Universal Fluctuations in Correlated Systems

TL;DR

This paper derives the analytical probability density function for the order parameter in the 2D-XY model and shows its applicability to a wide range of correlated systems, revealing universal fluctuation behavior.

Contribution

It provides the explicit analytical form of the PDF for the order parameter in the 2D-XY model and demonstrates its universality across various correlated systems.

Findings

The derived PDF matches fluctuations in multiple models.

Universal fluctuation behavior observed across systems.

Connections to Gaussian and extremal statistics discussed.

Abstract

The probability density function (PDF) of a global measure in a large class of highly correlated systems has been suggested to be of the same functional form. Here, we identify the analytical form of the PDF of one such measure, the order parameter in the low temperature phase of the 2D-XY model. We demonstrate that this function describes the fluctuations of global quantities in other correlated, equilibrium and non-equilibrium systems. These include a coupled rotor model, Ising and percolation models, models of forest fires, sand-piles, avalanches and granular media in a self organized critical state. We discuss the relationship with both Gaussian and extremal statistics.