Critical behavior of the weakly disordered Ising model: Six-loop ɛ expansion study

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 $4\ensuremath{-}\ensuremath{\varepsilon}$ space dimensions. For this purpose the ${\ensuremath{\phi}}^{4}$ field theory with cubic symmetry was analyzed in the replica limit $n\ensuremath{\rightarrow}0$. Along with renormalization group expansions in terms of renormalized couplings the $\sqrt{\ensuremath{\varepsilon}}$ 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 $\sqrt{\ensuremath{\varepsilon}}$ 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 $\sqrt{\ensuremath{\varepsilon}}$ series themselves turned out to be disappointing.