|
| | | | |
| | | |
| Stat |
Members: 3645
Articles: 2'501'711
Articles rated: 2609
20 April 2024 |
|
| | | | |
|
Article overview
| |
|
|
Dynamics of 2+1 dimensional SOS surfaces above a wall: slow mixing induced by entropic repulsion | | Pietro Caputo
; Eyal Lubetzky
; Fabio Martinelli
; Allan Sly
; Fabio Lucio Toninelli
; | | Date: |
31 May 2012 | | Abstract: | We study the Glauber dynamics for the (2+1)D Solid-On-Solid model above a
hard wall and below a far away ceiling, on an $L imes L$ box of $Z^2$ with
zero boundary conditions, at large inverse-temperature $eta$. It was shown by
Bricmont, El-Mellouki and Fr"ohlich (1986) that the floor constraint induces
an entropic repulsion effect which lifts the surface to an average height $H
asymp (1/eta)log L$. As an essential step in understanding the effect of
entropic repulsion on the Glauber dynamics we determine the equilibrium height
$H$ to within an additive constant: $H=(1/4eta)log L+O(1)$. We then show
that starting from zero initial conditions the surface rises to its final
height $H$ through a sequence of metastable transitions between consecutive
levels. The time for a transition from height $h=aH $, $ain (0,1)$, to height
$h+1$ is roughly $exp(c L^a)$ for some constant $c>0$. In particular, the
mixing time of the dynamics is exponentially large in $L$, i.e., $T_{mix} geq
e^{c L}$. We also provide the matching upper bound $T_{mix} leq e^{c’ L}$,
requiring a challenging analysis of the statistics of height contours at low
temperature and new coupling ideas and techniques. Finally, to emphasize the
role of entropic repulsion we show that without a floor constraint at height
zero the mixing time is no longer exponentially large in $L$. | | Source: | arXiv, 1205.6884 | | 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 Mozilla/5.0 AppleWebKit/537.36 (KHTML, like Gecko; compatible; ClaudeBot/1.0; +claudebot@anthropic.com)
|
| |
|
|
|
|
News, job offers and information for researchers and scientists:
| |
REGISTER