Freezing of dynamical exponents in low dimensional random media

Details Freezing of dynamical exponents in low dimensional random media Freezing of dynamical exponents in low dimensional random media

2000-06-23

arxiv.org/abs/cond-mat/0006373v1

Phys. Rev. Lett. {\bf 86} 4859 (2001)

Physics

Condensed Matter

5 pages, 2 figures, RevTex

Scientific paper

10.1103/PhysRevLett.86.4859

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 demonstrate that $T_{dyn}=T_c$, the static glass transition temperature, and that the dynamical exponent changes from $z(T)=2 + 2 (T_c/T)^2$ at high temperature to $z(T)= 4 T_c/T$ in the glass phase. The same formulae 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.

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