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arXiv · 2011.10782

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

M. V. Kompaniets·A. Kudlis·A. I. Sokolov
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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.

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M. V. Kompaniets, A. Kudlis, A. I. Sokolov. 2020-11-21. Critical behavior of weakly disordered Ising model: Six-loop $\sqrt \varepsilon$ expansion study. https://doi.org/10.1103/physreve.103.022134

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