Instability of the Random Fixed Point of Renormalization Group for the Spin Systems with Quenched Disorder

The replica trick used in the renormalization group (RG) for the disordered spin systems is discussed. The recursion relations of RG are derived in a more general situation in which the coupling constants can have arbitrary symmetry to the replica indices. It is shown that the random fixed point found by Luther, Grinstein and Lubensky is unstable. This instability implies that the replica symmetry should be broken in the RG for the disordered systems.