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Criterion for universality-class-independent critical fluctuations: example of the two-dimensional Ising model.

Research paper by Maxime M Clusel, Jean-Yves JY Fortin, Peter C W PC Holdsworth

Indexed on: 17 Dec '04Published on: 17 Dec '04Published in: Physical review. E, Statistical, nonlinear, and soft matter physics



Abstract

Order parameter fluctuations for the two-dimensional Ising model in the region of the critical temperature are presented. A locus of temperatures T(*) (L) and a locus of magnetic fields B(*) (L) are identified, for which the probability density function is similar to that for the two-dimensional XY model in the spin wave approximation. The characteristics of the fluctuations along these points are largely independent of universality class. We show that the largest range of fluctuations relative to the variance of the distribution occurs along these loci of points, rather than at the critical temperature itself and we discuss this observation in terms of intermittency. Our motivation is the identification of a generic form for fluctuations in correlated systems in accordance with recent experimental and numerical observations. We conclude that a universality-class-dependent form for the fluctuations is a particularity of critical phenomena related to the change in symmetry at a phase transition.