Critical behavior of weakly disordered Ising model: Six-loop $\sqrt \varepsilon$ expansion study

TL;DR

This study investigates the critical behavior of weakly disordered 3D Ising models using six-loop renormalization group expansions, providing numerical estimates that align well with experimental and simulation data.

Contribution

It introduces six-loop renormalization group expansions and $ oot extstyle rac{ ext{ extonehalf}}{ ext{ exttwothirds}}$ expansions for critical exponents in disordered Ising models, with improved numerical estimates.

Findings

Renormalization group expansions agree with experimental data.

Resummation of $ oot extstyle rac{ ext{ extonehalf}}{ ext{ exttwothirds}}$ series was ineffective.

Numerical estimates support the critical behavior predictions for disordered systems.

Abstract

The critical behavior of three-dimensional weakly diluted quenched Ising model is examined on the base of six-loop renormalization group expansions obtained within the minimal subtraction scheme in $4-\epsilon$ space dimensions. For this purpose the $\phi^4$ field theory with cubic symmetry was analyzed in the replica limit $n\rightarrow 0$. Along with renormalization group expansions in terms of renormalized couplings the $\sqrt{\varepsilon}$ expansions of critical exponents are presented. Corresponding numerical estimates for the physical, three-dimensional system are obtained by means of different resummation procedures applied both to the $\sqrt{\varepsilon}$ series and to initial renormalization group expansions. The results given by the latter approach are in a good agreement with their counterparts obtained experimentally and within the Monte Carlo simulations, while resumming of $\sqrt{\varepsilon}$ series themselves turned out to be disappointing.