Griffiths phase in diluted magnetic semiconductors

We study the effects of disorder in the vicinity of the ferromagnetic transition in a diluted magnetic semiconductor in the strongly localized regime. We derive an effective polaron Hamiltonian, which leads to the Griffiths phase above the ferromagnetic transition point. The Griffiths-McCoy effects yield non-perturbative contributions to the dynamic susceptibility. We explicitly derive the long-time susceptibility, which has a pseudo-scaling form, with the dynamic critical exponent being expressed through the percolation indices.