REPLICA SYMMETRY-BREAKING IN THE CRITICAL-BEHAVIOR IN THE M-COMPONENTFERROMAGNETIC SPIN SYSTEMS WITH A SHORT-RANGE DISORDER

We investigate the replica symmetry breaking (RSB) in m-component ferr omagnetic spin systems with a short-range disorder. Using epsilon-expa nsion the Landau-Ginzburg Hamiltonian with a RSB quartic interaction t erm is studied, where epsilon = 4 - d, d is the spatial dimension. The differential recursion relations of renormalization group (RG) are de rived to the second order of epsilon. The replicon eigenvalue, which i s a simple way to investigate the stability with respect to the contin uous RSB modes, is defined. The fixed points and their eigenvalues are obtained. For m < m(c) = 4 there is no stable fixed point. For m > m( c), 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 > m(c) only the pure fixed point is p hysical and stable. (C) 1998 Published by Elsevier Science B.V. All ri ghts reserved.