Critical behaviour of a 3D Ising-like system in the \rho^6 model approximation: Role of the correction for the potential averaging

TL;DR

This paper theoretically investigates the critical behavior of 3D Ising-like systems using the ho^6 model, highlighting the importance of potential averaging corrections in determining critical exponents.

Contribution

It introduces a correction for potential averaging into the ho^6 model, affecting critical exponents and providing a more accurate description of the system's critical behavior.

Findings

Nonzero critical exponent ta obtained

Renormalization of other critical exponents

Contribution of potential averaging correction to RG relations

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 \rho^6 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 \eta and the renormalization of the values of other critical exponents. The contributions from this correction to the recurrence relations for the \rho^6 model, fixed-point coordinates and elements of the renormalization-group linear transformation matrix are singled out. The expression for a small critical exponent \eta is obtained in a higher non-Gaussian approximation.