Self-similar replication approach to random-fields systems

Very long relaxation times are present in random-fields systems near their critical points. As the correlation length grows, already above the transition it is necessary to differentiate between the short-time (local) regime and the long-time (global) one. A self-similar replication procedure is proposed in order to separate iteratively between slow and fast modes. Recursion relations among effective exponents on successive time scales are obtained and apparent reduced dimensions, in both regimes, are deduced. For the short time behaviour of Ising systems we the authors find a dimensional reduction by one, both in d=3 and in d=2 (the lower critical dimension). The results are in agreement with the measurements of the specific heat and the correlation length performed on random antiferromagnets by linear birefringence and neutron scattering respectively.