| | |
| | |
Stat |
Members: 3643 Articles: 2'487'895 Articles rated: 2609
28 March 2024 |
|
| | | |
|
Article overview
| |
|
Time scale separation in the low temperature East model: Rigorous results | Paul Chleboun
; Alessandra Faggionato
; Fabio Martinelli
; | Date: |
12 Dec 2012 | Abstract: | We consider the non-equilibrium dynamics of the East model, a linear chain of
0-1 spins evolving under a simple Glauber dynamics in the presence of a kinetic
constraint which forbids flips of those spins whose left neighbour is 1. We
focus on the glassy effects caused by the kinetic constraint as $qdownarrow
0$, where $q$ is the equilibrium density of the 0’s. Specifically we analyse
time scale separation and dynamic heterogeneity, i.e. non-trivial
spatio-temporal fluctuations of the local relaxation to equilibrium, one of the
central aspects of glassy dynamics. For any mesoscopic length scale
$L=O(q^{-gamma})$, $gamma<1$, we show that the characteristic time scale
associated to two length scales $d/q^gamma$ and $d’/q^gamma$ are indeed
separated by a factor $q^{-a}$, $a=a(gamma)>0$, provided that $d’/d$ is large
enough independently of $q$. In particular, the evolution of mesoscopic
domains, i.e. maximal blocks of the form $111..10$, occurs on a time scale
which depends sharply on the size of the domain, a clear signature of dynamic
heterogeneity. Finally we show that no form of time scale separation can occur
for $gamma=1$, i.e. at the equilibrium scale $L=1/q$, contrary to what was
previously assumed in the physical literature based on numerical simulations. | Source: | arXiv, 1212.2956 | Services: | Forum | Review | PDF | Favorites |
|
|
No review found.
Did you like this article?
Note: answers to reviews or questions about the article must be posted in the forum section.
Authors are not allowed to review their own article. They can use the forum section.
browser claudebot
|
| |
|
|
|
| News, job offers and information for researchers and scientists:
| |