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

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 ${\varphi }^4$ field theory with cubic symmetry was analyzed in the replica limit $n\to 0$. Along with renormalization group expansions in terms of renormalized couplings the $\sqrt{\epsilon }$ 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 $\sqrt{\epsilon }$ 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 $\sqrt{\epsilon }$ series themselves turned out to be disappointing.

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• Extrapolation from hypergeometric functions, continued functions and Borel-Leroy transformation; Resummation of perturbative renormalization functions from field theories
• Continued functions and critical exponents: Tools for analytical continuation of divergent expressions in phase transition studies
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• Critical exponents of the Ising model with quenched structural disorder and long-range interactions at spatial dimension $d=3$