Depinning of a polymer in a multi-interface medium
Abstract
In this paper we consider a model which describes a polymer chain interacting with an infinity of equi-spaced linear interfaces. The distance between two consecutive interfaces is denoted by T = T_N and is allowed to grow with the size N of the polymer. When the polymer receives a positive reward for touching the interfaces, its asymptotic behavior has been derived in a previous paper, showing that a transition occurs when T_N \approx log(N). In the present paper, we deal with the so-called depinning case, i.e., the polymer is repelled rather than attracted by the interfaces. Using techniques from renewal theory, we determine the scaling behavior of the model for large N as a function of T_N, showing that two transitions occur, when T_N \approx N^{1/3} and when T_N \approx N^{1/2} respectively.
- Publication:
-
arXiv e-prints
- Pub Date:
- January 2009
- DOI:
- 10.48550/arXiv.0901.2902
- arXiv:
- arXiv:0901.2902
- Bibcode:
- 2009arXiv0901.2902C
- Keywords:
-
- Mathematics - Probability;
- 60K35;
- 60F05;
- 82B41
- E-Print:
- 27 pages, 2 figures