forgot password?
register here
Research articles
  search articles
  reviews guidelines
  articles index
My Pages
my alerts
  my messages
  my reviews
  my favorites
Members: 2831
Articles: 1'984'581
Articles rated: 2574

13 August 2020
  » 1025271

 Article forum

Spiral Model: a cellular automaton with a discontinuous glass transition
Cristina Toninelli ; Giulio Biroli ;
Date 4 Sep 2007
AbstractWe introduce a new class of two-dimensional cellular automata with a bootstrap percolation-like dynamics. Each site can be either empty or occupied by a single particle and the dynamics follows a deterministic updating rule at discrete times which allows only emptying sites. We prove that the threshold density $ ho_c$ for convergence to a completely empty configuration is non trivial, $0< ho_c<1$, contrary to standard bootstrap percolation. Furthermore we prove that in the subcritical regime, $ ho< ho_c$, emptying always occurs exponentially fast and that $ ho_c$ coincides with the critical density for two-dimensional oriented site percolation on $Z^2$. This is known to occur also for some cellular automata with oriented rules for which the transition is continuous in the value of the asymptotic density and the crossover length determining finite size effects diverges as a power law when the critical density is approached from below. Instead for our model we prove that the transition is {it discontinuous} and at the same time the crossover length diverges {it faster than any power law}. The proofs of the discontinuity and the lower bound on the crossover length use a conjecture on the critical behaviour for oriented percolation. The latter is supported by several numerical simulations and by analytical (though non rigorous) works through renormalization techniques. Finally, we will discuss why, due to the peculiar {it mixed critical/first order character} of this transition, the model is particularly relevant to study glassy and jamming transitions. Indeed, we will show that it leads to a dynamical glass transition for a Kinetically Constrained Spin Model. Most of the results that we present are the rigorous proofs of physical arguments developed in a joint work with D.S.Fisher.
Source arXiv, 0709.0378
Services Forum | Review | PDF | Favorites   

No message found in this article forum.  You have a question or message about this article? Ask the community and write a message in the forum.
If you want to rate this article, please use the review section..

Subject of your forum message:
Write your forum message below (min 50, max 2000 characters)

2000 characters left.
Please, read carefully your message since you cannot modify it after submitting.

  To add a message in the forum, you need to login or register first. (free): registration page
» my Online CV
» Free

News, job offers and information for researchers and scientists:
home  |  contact  |  terms of use  |  sitemap
Copyright © 2005-2020 - Scimetrica