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Universality for critical kinetically constrained models: infinite number of stable directions | | Ivailo Hartarsky
; Laure Marêché
; Cristina Toninelli
; | | Date: |
19 Apr 2019 | | Abstract: | Kinetically constrained models (KCM) are reversible interacting particle
systems on $mathbb{Z}^d$ with continuous-time constrained Glauber dynamics.
They are a natural non-monotone stochastic version of the family of cellular
automata with random initial state known as $mathcal{U}$-bootstrap
percolation. KCM have an interest in their own right, owing to their use for
modelling the liquid-glass transition in condensed matter physics.
In two dimensions there are three classes of models with qualitatively
different scaling of the infection time of the origin as the density of
infected sites vanishes. Here we study in full generality the class termed
’critical’. Together with the companion paper by Martinelli and two of the
authors we establish the universality classes of critical KCM and determine
within each class the critical exponent of the infection time as well as of the
spectral gap. In this work we prove that for critical models with an infinite
number of stable directions this exponent is twice the one of their bootstrap
percolation counterpart. This is due to the occurrence of ’energy barriers’,
which determine the dominant behaviour for these KCM but which do not matter
for the monotone bootstrap dynamics. Our result confirms the conjecture of
Martinelli, Morris and the last author, who proved a matching upper bound. | | Source: | arXiv, 1904.9145 | | Services: | Forum | Review | PDF | Favorites | |
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