Europhys. Lett., 76 (6), pp. 1008-1014 (2006)
DOI: 10.1209/epl/i2006-10395-x

Origin of the approximate universality of distributions in equilibrium correlated systems

M. Clusel¹, J.-Y. Fortin² and P. C. W. Holdsworth<sup>3

1</sup>  Institut Laue-Langevin - 6 rue J. Horowitz, 38042 Grenoble cedex, France
²  Laboratoire Poncelet, CNRS/UMI 2615 - Bolshoy Vlasyevskiy Pereulok 11 Moscow 119002, Russia
³  Laboratoire de Physique, École normale supérieure de Lyon 46, Allée d'Italie, 69007 Lyon, France

received 17 May 2006; accepted in final form 25 October 2006
published online 23 November 2006

Abstract
We propose an interpretation of previous experiments 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 (BRAMWELL S. T. ET AL. , Nature, 396 (1998) 512). This approach, developed for the Ising model, is based on previous numerical observations (CLUSEL M. ET AL. , Phys. Rev. E, 70 (2004) 046112). 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.

PACS
05.40.-a - Fluctuation phenomena, random processes, noise, and Brownian motion.
05.70.Fh - Phase transitions: general studies.
05.20.-y - Classical statistical mechanics.

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