PINNING AND WETTING TRANSITION FOR (1+1)-DIMENSIONAL FIELDS WITH LAPLACIAN INTERACTION

• 成果类型: Article
• 署名作者: Caravenna, Francesco; Deuschel, Jean-Dominique
• 署名单位: University of Padua; Technical University of Berlin
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/08-AOP395
• 发表日期: 2008
• 页码: 2388-2433
• 关键词: polymer depinning transitions; dna denaturation transition; semiflexible polymers; entropic repulsion; models; copolymers; disorder

摘要

We consider a random field phi : {1,..., N} -> R as a model fora linear chain attracted to the defect line phi = 0. that is, the x-axis. The free law of the field is specified by the density exp(-Sigma(i) V(Delta phi(i))) with respect to the Lebesgue measure on R(N), where Delta is the discrete Laplacian and we allow for a very large class of potentials V(.). The interaction with the defect line is introduced by giving the field a reward epsilon >= 0 each time it touches the x-axis. We call this model the pinning model. We consider a second model, the wetting model, in which, in addition to the pinning reward, the field is also constrained to stay nonnegative. We show that both models Under-go a phase transition as the intensity epsilon of the pinning reward varies: both in the pinning (a = p) and in the wetting (a = w) case. there exists a critical value epsilon(a)(c) Such that when epsilon > epsilon(a)(c) the field touches the defect line a positive fraction of times (localization). while this does not happen for epsilon < epsilon(a)(c) (delocalization). The two critical values Lire nontrivial and distinct. 0 < epsilon(p)(c) < epsilon(w)(c) < infinity, and they are the only nonanalyticity points of the respective free energies. For the pinning model the transition is of second order. hence the field at epsilon = epsilon(p)(c) is delocalized. On the other hand. the transition in the wetting model is of first order and for epsilon = epsilon(w)(c) the field is localized. The core of our approach is a Markov renewal theory description of the field.