Eur. Phys. J. B (2012) 85: 122
https://doi.org/10.1140/epjb/e2012-30057-7

Regular Article

Probability distribution function of dipolar field in two-dimensional spin ensemble

Institute of Automation and Control Processes, Far East Branch of Russian Academy of Sciences, 5, Radio st., 690041 Vladivostok, Russia

^a e-mail: panov@iacp.dvo.ru

Received: 14 September 2011
Received in final form: 23 January 2012
Published online: 13 April 2012

Abstract

We theoretically determine the probability distribution function of the net field of the random planar structure of dipoles which represent polarized particles. At small surface concentrations c of the point dipoles this distribution is expressed in terms of special functions. At the surface concentrations of the dipoles as high as 0.6 the dipolar field obey the Gaussian law. To obtain the distribution function within transitional region c < 0.6, we propose the method based on the cumulant expansion. We calculate the parameters of the distributions for some specific configurations of the dipoles. The distribution functions of the ordered ensembles of the dipoles at the low and moderate surface concentrations have asymmetric shape with respect to distribution medians. The distribution functions allow to calculate various physical parameters of two-dimensional interacting nanoparticle ensembles.