Pinning of polymers and interfaces by random potentials
| dc.creator | Alexander, Kenneth S. | |
| dc.creator | Sidoravicius, Vladas | |
| dc.date | 2005-01-03 | |
| dc.date | 2006-07-05 | |
| dc.date.accessioned | 2026-07-07T06:39:14Z | |
| dc.date.available | 2026-07-07T06:39:14Z | |
| dc.description | We consider a polymer, with monomer locations modeled by the trajectory of a Markov chain, in the presence of a potential that interacts with the polymer when it visits a particular site 0. Disorder is introduced by, for example, having the interaction vary from one monomer to another, as a constant $u$ plus i.i.d. mean-0 randomness. There is a critical value of $u$ above which the polymer is pinned, placing a positive fraction of its monomers at 0 with high probability. This critical point may differ for the quenched, annealed and deterministic cases. We show that self-averaging occurs, meaning that the quenched free energy and critical point are nonrandom, off a null set. We evaluate the critical point for a deterministic interaction ($u$ without added randomness) and establish our main result that the critical point in the quenched case is strictly smaller. We show that, for every fixed $u\in\mathbb{R}$, pinning occurs at sufficiently low temperatures. If the excursion length distribution has polynomial tails and the interaction does not have a finite exponential moment, then pinning occurs for all $u\in\mathbb{R}$ at arbitrary temperature. Our results apply to other mathematically similar situations as well, such as a directed polymer that interacts with a random potential located in a one-dimensional defect, or an interface in two dimensions interacting with a random potential along a wall. | |
| dc.description | Published at http://dx.doi.org/10.1214/105051606000000015 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org) | |
| dc.identifier | https://arxiv.org/abs/math/0501028 | |
| dc.identifier | http://arxiv.org/abs/math/0501028 | |
| dc.identifier | Annals of Applied Probability 2006, Vol. 16, No. 2, 636-669 | |
| dc.identifier | doi:10.1214/105051606000000015 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/101005 | |
| dc.subject | Probability | |
| dc.subject | Statistical Mechanics | |
| dc.subject | Mathematical Physics | |
| dc.subject | 82D60 (Primary) 82B44, 60K35 (Secondary) | |
| dc.title | Pinning of polymers and interfaces by random potentials | |
| dc.type | text |