# The Asymmetric One-Dimensional Constrained Ising Model: Rigorous Results

@article{Aldous2002TheAO, title={The Asymmetric One-Dimensional Constrained Ising Model: Rigorous Results}, author={David J. Aldous and Persi Diaconis}, journal={Journal of Statistical Physics}, year={2002}, volume={107}, pages={945-975} }

AbstractWe study a one-dimensional spin (interacting particle) system, with product Bernoulli (p) stationary distribution, in which a site can flip only when its left neighbor is in state +1. Such models have been studied in physics as simple exemplars of systems exhibiting slow relaxation. In our “East” model the natural conjecture is that the relaxation time τ(p), that is 1/(spectral gap), satisfies log τ(p)∼
$$\tfrac{{\log ^2 (1/p)}}{{\log 2}}$$
as p↓0. We prove this up to a factor of 2…

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