Origin of the approximate universality of distributions in equilibrium correlated systems

¹ 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: 25 October 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.