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22 September 2020
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Glassy dynamics in the East model
P. Sollich ; M. R. Evans ;
Date 17 Mar 2003
Journal Physical Review E, 68:031504, 2003 DOI: 10.1103/PhysRevE.68.031504
Subject Statistical Mechanics; Disordered Systems and Neural Networks | cond-mat.stat-mech cond-mat.dis-nn
AbstractWe 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 neighbour is up. We give details of our previous solution of the non-equilibrium 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 $ar{d} sim t^{T ln 2}$, and the pronounced `fragile glass’-divergence of equilibration times as $t_*=exp(1/T^2ln 2)$. 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 timescales and lengthscales, we propose a model for the dynamics of `superdomains’ which are bounded by up-spins that are frozen on long timescales. From this we deduce that the equilibrium spin correlation and persistence functions should exhibit identical scaling behaviour for low $T$, decaying as $g( ilde{t})$. The scaling variable is $ ilde{t}=(t/t_*)^{Tln 2}$, giving strongly stretched behaviour for low $T$. The scaling function $g(cdot)$ decays faster than exponential, however, and in the limit $T o 0$ at fixed $ ilde{t}$ reaches zero at a {em finite} value of $ ilde{t}$.
Source arXiv, cond-mat/0303318
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