Correlated random-field systems: Dissipative dynamics and phenomenological scaling

Abstract

We investigate a $(d+1)$-dimensional ``correlated'' random-field system with d spatial dimensions and one Trotter dimension along which randomness is ``correlated'' or striped. In the sense of universality this model is equivalent to a d-dimensional quantum random-field system. We investigate the dissipative Langevin dynamics of this ``striped'' $(d+1)$-dimensional systems within a replica symmetric framework, employing the perturbative $\ensuremath{\epsilon}$ expansion around the upper critical dimension to explore the effect of an additional dimension (along which the randomness is correlated) on the dynamical scaling. We argue that the $\ensuremath{\epsilon}$ expansion fails to capture the activated nature of dynamics. We also extend the phenomenological renormalization-group calculations to investigate the critical behavior of a $(d+1)$-dimensional correlated random-field Ising systems.