Equilibrium critical properties of random field systems : new conjectures

Abstract

In order to account for experimentally observed qualitative properties of random field Ising systems, a new picture of transitions in systems with frozen disorder is suggested. According to this picture, equilibration processes near Tc require activated jumps between remote free energy wells in the phase space. These jumps involve very slow dynamics, described by a modified Vogel-Fulcher law for the relaxation time τ ∼ exp[Const./( T - Tc)Z]. The theory depends upon 3 critical exponents. The new exponent corresponds, as remarked by Krey, to random field renormalization. The inequalities satisfied by the exponents are investigated, as well as the equalities which give the other exponents. Classical concepts, such as dimensional reduction, are criticized. The exponent η' corresponds, if our picture is correct, to thermal fluctuations between remote wells, a novel effect which seems to be incompatible with dimensional reduction