Glassy dynamics in the asymmetrically constrained kinetic Ising chain.
We study the dynamics of the East model, comprising a chain of uncoupled spins in a downward-pointing field. Glassy effects arise at low temperatures T from the kinetic constraint that spins can only flip if their left neighbor is up. We give details of our previous solution of the nonequilibrium coarsening dynamics after a quench to low T [Phys. Rev. Lett. 83, 3238 (1999)], including the anomalous coarsening of down-spin domains with typical size d approximately t(T ln 2), and the pronounced "fragile glass" divergence of equilibration times as t(*)=exp(1/T(2) ln 2). We also link the model to the paste-all coarsening model, defining a family of interpolating models that all have the same scaling distribution of domain sizes. We then proceed to the problem of equilibrium dynamics at low T. Based on a scaling hypothesis for the relation between time scales and length scales, we propose a model for the dynamics of "superdomains" which are bounded by up-spins that are frozen on long time scales. From this we deduce that the equilibrium spin correlation and persistence functions should exhibit identical scaling behavior for low T, decaying as g(t). The scaling variable is t=(t/t(*))(T ln 2), giving strongly stretched behavior for low T. The scaling function g(.) decays faster than exponential, however, and in the limit T-->0 at fixed t reaches zero at a finite value of t.
Sollich
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P
Department of Mathematics, Kings College London, Strand, London WC2R 2LS, United Kingdom.
Evans
M R
MR