title: Freezing of dynamical exponents in low dimensional random media.
abstract: A particle in a random potential with logarithmic correlations in dimensions d = 1,2 is shown to undergo a dynamical transition at T(dyn)>0. In d = 1 exact results show T(dyn) = T(c), the static glass transition temperature, and that the dynamical exponent changes from z(T) = 2+2(T(c)/T)(2) at high T to z(T) = 4T(c)/T in the glass phase. The same formulas are argued to hold in d = 2. Dynamical freezing is also predicted in the 2D random gauge XY model and related systems. In d = 1 a mapping between dynamics and statics is unveiled and freezing involves barriers as well as valleys. Anomalous scaling occurs in the creep dynamics, relevant to dislocation motion experiments.
authors.affiliation: CNRS-Laboratoire de Physique Théorique de l'Ecole Normale Supérieure, 24 rue Lhomond, 75231 Cedex 05, Paris, France.
authors.forename: H E
authors.initials: HE
authors.lastname: Castillo
authors.forename: P
authors.initials: P
authors.lastname: Le Doussal