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Mixing time bounds for oriented kinetically constrained spin models | Paul Chleboun
; Fabio Martinelli
; | Date: |
21 Dec 2012 | Abstract: | We analyze the mixing time of a class of oriented kinetically constrained
spin models (KCMs) on a d-dimensional lattice of $n^d$ sites. A typical example
is the North-East model, a 0-1 spin system on the two-dimensional integer
lattice that evolves according to the following rule: whenever a site’s
southerly and westerly nearest neighbours have spin 0, with rate one it resets
its own spin by tossing a p-coin, at all other times its spin remains frozen.
Such models are very popular in statistical physics because, in spite of their
simplicity, they display some of the key features of the dynamics of real
glasses. We prove that the mixing time is O(n log n) whenever the relaxation
time is O(1). Our study was motivated by the "shape" conjecture put forward by
G. Kordzakhia and S.P. Lalley. | Source: | arXiv, 1212.5425 | Services: | Forum | Review | PDF | Favorites |
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