Critical behaviour of a 3D Ising-like system in the ρ⁶ model approximation: Role of the correction for the potential averaging

Abstract

The critical behaviour of systems belonging to the three-dimensional Ising universality class is studied theoretically using the collective variables (CV) method. The partition function of a one-component spin system is calculated by the integration over the layers of the CV phase space in the approximation of the non-Gaussian sextic distribution of order-parameter fluctuations (the ρ6 model). A specific feature of the proposed calculation consists in making allowance for the dependence of the Fourier transform of the interaction potential on the wave vector. The inclusion of the correction for the potential averaging leads to a nonzero critical exponent of the correlation function η and the renormalization of the values of other critical exponents. The contributions from this correction to the recurrence relations for the ρ6 model, fixed-point coordinates and elements of the renormalization-group linear transformation matrix are singled out. The expression for a small critical exponent η is obtained in a higher non-Gaussian approximation.

Keywords

• three-dimensional Ising-like system
• critical behaviour
• sextic distribution
• potential averaging
• small critical exponent