Order parameter of a three-dimensional Ising-like system in the simplest and higher non-Gaussian approximations

Abstract

The application of the collective variables method to the study of the behaviour of nonuniversal characteristics of the system in the critical region is illustrated by an example of the order parameter. Explicit expressions for the order parameter (the average spin moment) of a three-dimensional uniaxial magnet are obtained in approximations of quartic and sextic non-Gaussian fluctuation distributions (the ρ 4 and ρ 6 models, respectively), taking into account confluent corrections. Some distinctive features appearing in the process of calculating the order parameter on the basis of two successive non-Gaussian approximations are indicated. The dependence of the average spin moment of an Ising-like system on the temperature and microscopic parameters is studied.

Critical line of the Φ^4 scalar field theory on a 4D cubic lattice in the local potential approximation

“…The link between these two formulations can however be established, see for instance references [15,16]. Other non-perturbative methods based either on the CV or Monte Carlo methods are also the subject of active studies and are discussed, for instance, in reference [17] and references quoted herein.…”