The Asymmetric One-Dimensional Constrained Ising Model

Abstract

We study a reversible one-dimensional spin system with Bernoulli(p) stationary distribution, in which a site can flip only if the site to its left is in state +1. Such models have been used as simple exemplars of systems exhibiting slow relaxation. We give fairly sharp estimates of the spectral gap as p decreases to zero. The method uses Poincare comparison with a long-range process which is analyzed by probabilistic methods (coupling, supermartingales).

32 pages

References in corpus (1)

• Glassy timescale divergence and anomalous coarsening in a kinetically constrained spin chain

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