Replica symmetry breaking in critical phenomena in long-range disordered ferromagnets

The replica symmetry breaking (RSB) is investigated in m-component ferromag netic spin systems with a long-range disorder, with a correlation function obeying a power law similar to s(-a). The Landau-Ginzburg Hamiltonian with an RSB quartic interaction term is studied, with the renormalization-group expansion in epsilon = 4 - D and delta = 4 - a, where D is the spatial dime nsion. It is shown that the long-range disorder fixed point found previousl y is unstable under the perturbation of RSB for m < 4 and stable for m grea ter than or equal to 4. The RSB fixed points are calculated and there is no physical stable fixed point for m < 4.