Critical behavior of crystals with long-range correlations caused by point defects with degenerate internal degrees of freedom

We analyze the possibility of the appearance of long-range correlations of states of quenched defect systems in disordered solids. For randomly distributed defects with a finite number of degenerate internal degrees of freedom such correlations are shown to appear near the defect percolation threshold if they obey certain nearest-neighbor correlation rules. The corresponding effective Hamiltonian can be viewed as that of a generalized m-component long-range correlated Weinrib-Halperin model. Our renormalization-group investigation shows, however, that it asymptotically decomposes into a set of m noninteracting one-component Weinrib-Halperin models. The coordinates of the stable fixed point of this model are determined to O(ε1/2).