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We study the critical properties of the weakly disordered $p$-componentrandom Heisenberg ferromagnet. It is shown that if the specific heat criticalexponent of the pure system is positive, the traditional renormalization group(RG) flows at dimensions $D=4-\e$, which are usually considered as describingthe disorder-induced universal critical behavior, are {\it unstable} withrespect to replica symmetry breaking (RSB) potentials as found in spin glasses.It is demonstrated that the RG flows involving RSB potentials lead to fixedpoints which have the structure known as the 1 step RSB, and there exists awhole spectrum of such fixed points. It is argued that spontaneous RSB canoccur due to the interactions of the fluctuating fields with the localnon-perturbative degrees of freedom coming from the multiple local minimasolutions of the mean-field equations. However, it is not clear whether or notRSB occurs for infinitesimally weak disorder. Physical consequences of theseconclusions are discussed.Comment: 20 pages, late

Replica-symmetry breaking in the critical behaviour of the random ferromagnet