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Nonlinear Langevin equation; phase transition; critical exponent; cumulant expansion; Gaussian decoupling

A stochastic model of cooperative behaviour is analyzed with regard to its critical properties. A cumulant expansion to fourth order is used to truncate the infinite set of coupled evolution equations for the moments. Linear stability analysis is performed around all the permissible steady states. The method is shown to be incapable of reproducing the critical boundary and the nature of the phase transition. A linearization, which respects the symmetry of the potential, is proposed which reproduces all the basic features associated with the model. The dynamics predicted by this approximation is shown to agree well with the Monte-Carlo simulation of the nonlinear Langevin equation.

M C Valsakumar¹

1. Materials Science Laboratory, Indira Gandhi Centre for Atomic Research, Kalpakkam - 603 102, India

Published

May 1986

Manuscript received

2 December 1985

Manuscript revised

17 February 1986