Replica Symmetry Breaking in the Critical Behaviour 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 critical exponent of the pure system is positive, the traditional renormalization group (RG) flows at dimensions $D=4-\e$, which are usually considered as describing the disorder-induced universal critical behavior, are {\it unstable} with respect to replica symmetry breaking (RSB) potentials as found in spin glasses. It is demonstrated that the RG flows involving RSB potentials lead to fixed points which have the structure known as the 1 step RSB, and there exists a whole spectrum of such fixed points. It is argued that spontaneous RSB can occur due to the interactions of the fluctuating fields with the local non-perturbative degrees of freedom coming from the multiple local minima solutions of the mean-field equations. However, it is not clear whether or not RSB occurs for infinitesimally weak disorder. Physical consequences of these conclusions are discussed. 
Viktor Dotsenko, A. B. Harris, David Sherrington and R. B. Stinchcombe