Five-loop renormalization-group expansions for the three-dimensional n-vector cubic model and critical exponents for impure Ising systems

TL;DR

This paper computes five-loop RG functions for the three-dimensional n-vector cubic model and derives high-precision critical exponents for impure Ising systems using advanced resummation techniques.

Contribution

It provides the first five-loop RG series calculations for the 3D n-vector cubic model and refines critical exponent estimates for impure Ising systems.

Findings

Critical exponents for impure Ising systems with high precision.

Five-loop RG series calculations for the cubic model.

Estimated correction-to-scaling exponent  = 0.32  

Abstract

The renormalization-group (RG) functions for the three-dimensional n-vector cubic model are calculated in the five-loop approximation. High-precision numerical estimates for the asymptotic critical exponents of the three-dimensional impure Ising systems are extracted from the five-loop RG series by means of the Pade-Borel-Leroy resummation under n = 0. These exponents are found to be: \gamma = 1.325 +/- 0.003, \eta = 0.025 +/- 0.01, \nu = 0.671 +/- 0.005, \alpha = - 0.0125 +/- 0.008, \beta = 0.344 +/- 0.006. For the correction-to-scaling exponent, the less accurate estimate \omega = 0.32 +/- 0.06 is obtained.