Pinning of polymers and interfaces by random potentials

被引:30
作者
Alexander, Kenneth S. [1 ]
Sidoravicius, Vladas
机构
[1] Univ So Calif, Dept Math KAP 108, Los Angeles, CA 90089 USA
[2] Inst Matematica Pura & Aplicada, BR-22460320 Rio De Janeiro, Brazil
关键词
pinning; polymer; disorder; interface; random potential;
D O I
10.1214/105051606000000015
中图分类号
O21 [概率论与数理统计]; C8 [统计学];
学科分类号
020208 ; 070103 ; 0714 ;
摘要
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 epsilon 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 epsilon 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.
引用
收藏
页码:636 / 669
页数:34
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