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We study the critical properties of the weakly disordered $p$-componentferromagnet in terms of the renormalization group (RG) theory generalized totake into account the replica symmetry breaking (RSB) effects coming from themultiple local minima solutions of the mean-field equations. It is shown thatfor $p < 4$ the traditional RG flows at dimensions $D=4-\epsilon$, which areusually considered as describing the disorder-induced universal criticalbehavior, are unstable with respect to the RSB potentials as found in spinglasses. It is demonstrated that for a general type of the Parisi RSBstructures there exists no stable fixed points, and the RG flows lead to the{\it strong coupling regime} at the finite scale $R_{*} \sim \exp(1/u)$, where$u$ is the small parameter describing the disorder. The physical concequencesof the obtained RG solutions are discussed. In particular, we argue, thatdiscovered RSB strong coupling phenomena indicate on the onset of a new spinglass type critical behaviour in the temperature interval $\tau < \tau_{*} \sim\exp(-1/u)$ near $T_{c}$. Possible relevance of the considered RSB effects forthe Griffith phase is also discussed.Comment: 32 pages, Late

Replica symmetry breaking and the renormalization group theory of the weakly disordered ferromagnet