Replica symmetry breaking in the critical behavior in the m-component ferromagnetic spin systems with a short-range disorder

We investigate the replica symmetry breaking (RSB) in m-component ferromagnetic spin systems with a short-range disorder. Using ε-expansion the Landau–Ginzburg Hamiltonian with a RSB quartic interaction term is studied, where ε=4−d, d is the spatial dimension. The differential recursion relations of renormalization group (RG) are derived to the second order of ε. The replicon eigenvalue, which is a simple way to investigate the stability with respect to the continuous RSB modes, is defined. The fixed points and their eigenvalues are obtained. For mmc, we find a stable fixed point, which is not only stable in the one-step RSB subspace but also stable with respect to the continuous RSB. However, it is unphysical. For m>mc only the pure fixed point is physical and stable.