2003/03/31 by P. Sollich, Peter Sollich, M. R. Evans
Materials Science · Physics and Astronomy · #Material Dynamics and Properties #Quantum many-body systems #Theoretical and Computational Physics #cond-mat.dis-nn #cond-mat.stat-mech
paper · pdf · doi:10.1103/physreve.68.031504
published as Physical Review E, 68:031504, 2003 · 17 pages, revtex4, 8 figures. Minor clarifications, plus new figure 6 to provide simulation support for the notion of superdomain dynamics
arxiv created 2003/05/21 · openalex publication_date 2003/09/26 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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\ensuremath∼tTln2, and the pronounced ``fragile glass'' divergence of equilibration times as t*=exp(1/T2ln2). 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(\stackrel\ifmmode \else \~\fit). The scaling variable is \stackrel\ifmmode \else \~\fit=(t/t*)Tln2, giving strongly stretched behavior for low T. The scaling function g(\ensuremath⋅) decays faster than exponential, however, and in the limit \stackrel\ensuremath→T0 at fixed \stackrel\ifmmode \else \~\fit reaches zero at a finite value of \stackrel\ifmmode \else \~\fit.