Universal Fluctuations in Correlated Systems

S. T. Bramwell; K. Christensen; J.-Y. Fortin; P. C. W. Holdsworth; H. J. Jensen; S. Lise; J. M. López; M. Nicodemi; J.-F. Pinton; M. Sellitto

doi:10.1103/PhysRevLett.84.3744

Universal Fluctuations in Correlated Systems

S. T. Bramwell, K. Christensen, J.-Y. Fortin, P. C. W. Holdsworth, H. J. Jensen, S. Lise, J. M. López, M. Nicodemi, J.-F. Pinton, and M. Sellitto

Phys. Rev. Lett. 84, 3744 – Published 24 April 2000

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 nonequilibrium systems. These include a coupled rotor model, Ising and percolation models, models of forest fires, sandpiles, avalanches, and granular media in a self-organized critical state. We discuss the relationship with both Gaussian and extremal statistics.

Received 15 December 1999

DOI:https://doi.org/10.1103/PhysRevLett.84.3744

Authors & Affiliations

S. T. Bramwell¹, K. Christensen², J.-Y. Fortin^3,*, P. C. W. Holdsworth⁴, H. J. Jensen⁵, S. Lise⁵, J. M. López^5,†, M. Nicodemi⁵, J.-F. Pinton⁴, and M. Sellitto⁴

¹Department of Chemistry, University College London, 20 Gordon Street, London WC1H 0AJ, United Kingdom
²Blackett Laboratory, Imperial College, Prince Consort Road, London SW7 2BZ, United Kingdom
³Department of Physics, University of Washington, Box 351560, Seattle, Washington 98195-1560
⁴Laboratoire de Physique, Ecole Normale Supérieure, 46 Allée d'Italie, F-69364 Lyon Cedex 07, France
⁵Department of Mathematics, Huxley Building Imperial College, 180 Queen's Gate, London SW7 2BZ, United Kingdom

^*Permanent address: CNRS, UMR 7085, Laboratoire de Physique Théorique, Université Louis Pasteur, 67084 Strasbourg, France.
^†Present address: Dipartamento di Fisica and Unità INFM, Università di Roma “La Sapienza,” Piazzale A. Moro 2, Roma I-00185, France.