Replica-space renormalization in random-field systems

Abstract

The critical behavior of random-field systems is characterized by exponentially long relaxation times. They may differ by orders of magnitude and slow modes have to be considered quenched with respect to the faster ones. This requires a drastic modification of the renormalization process in which the degrees of freedom are integrated out. A new replica-space renormalization procedure, to carry out the coarse-graining of the time intervals, is presented. We relate by recursion-relations the effective reduced dimensions of consecutive time scales. Their stable fixed-points yield the apparent dimensionalities for the longest and shortest time scales, which are insentive to the exact behavior on intermediate scales. For Ising systems we find that d = 2 is the lower critical dimension in both regimes. The thermal exponents for d = 3, in the short-time observable regime, are related to those of the pure system in d = 2. This is consistent with the observations in field-cooled random antiferromagnets of the correlation length exponent v ≈ 1 (by neutron scattering) and of the symmetric logarithmic divergence in the specific-heat (by linear birefringence).