REPLICA-SYMMETRY BREAKING IN THE CRITICAL-BEHAVIOR OF THE RANDOM FERROMAGNET

We study the critical properties of the weakly disordered p-component random Heisenberg ferromagnet. It is shown that if the specific-heat c ritical exponent of the pure system is positive, the traditional renor malization group (RG) hows at dimensions D = 4 - epsilon, which are us ually considered as describing the disorder-induced universal critical behaviour, are unstable with respect to replica-symmetry breaking (RS B) potentials such as those found in spin glasses. It is demonstrated that the Ro flows involving RSB potentials lead to fixed points which have a structure known as the one-step RSB, and there exists a whole s pectrum of such fixed points. It is argued that spontaneous RSB can oc cur due to the interactions of the fluctuating fields with the local n on-perturbative degrees of freedom coming from the multiple local mini ma solutions of the mean-field equations. However, it is not clear whe ther or not RSB occurs for infinitesimally weak disorder. Physical con sequences of these conclusions are discussed.