Eur. Phys. J. B (2012) 85: 16
https://doi.org/10.1140/epjb/e2011-20588-8

Regular Article

Expansion of the Glauber equation of motion in terms of cumulants powers

Statistical properties of the Glauber equation of motion

Service OPERA (CP194/5), Université libre de Bruxelles, Avenue F.D. Roosevelt 50, 1050 Brussels, Belgium

^a e-mail: tbury@ulb.ac.be

Received: 19 July 2011
Received in final form: 4 November 2011
Published online: 18 January 2012

Abstract

We present an expansion of the Glauber equation of motion in terms of cumulants of the effective fields. We show that we recover a part of the fluctuations with a simple third order expansion. We illustrate the method with an application to the 2D square lattice Ising model with nearest neighbors. For the special case of perturbed non gaussian effective fields, we show that only the first cumulants are significative. Furthermore it can be shown that the resulting distribution is closer to the normal distribution than the unperturbed fields one. It leads to the conclusion that we can consistently truncate the expansion of the exact Glauber equation of motion.