Phase transitions for spatially extended pinning

• 成果类型: Article
• 署名作者: Caravenna, Francesco; den Hollander, Frank
• 署名单位: University of Milano-Bicocca; Leiden University - Excl LUMC; Leiden University
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-021-01068-y
• 发表日期: 2021
• 页码: 329-375
• 关键词: variational characterization; copolymer; polymer; limit; disorder

摘要

We consider a directed polymer of length N interacting with a linear interface. The monomers carry i.i.d. random charges (omega(i))(i=1)(N) taking values in R with mean zero and variance one. Each monomer i contributes an energy (beta omega(i) - h)phi(S-i) to the interaction Hamiltonian, where S-i is an element of Z is the height of monomer i with respect to the interface, phi : Z -> [0, infinity) is the interaction potential, beta is an element of [0, infinity) is the inverse temperature, and h is an element of R is the charge bias parameter. The configurations of the polymer are weighted according to theGibbs measure associated with the interactionHamiltonian, where the reference measure is given by aMarkov chain onZ. We study both the quenched and the annealed free energy per monomer in the limit as N -> infinity. We showthat each exhibits a phase transition along a critical curve in the (beta, h)-plane, separating a localized phase (where the polymer stays close to the interface) from a delocalized phase (where the polymer wanders away from the interface). We derive variational formulas for the critical curves and we obtain upper and lower bounds on the quenched critical curve in terms of the annealed critical curve. In addition, for the special case where the reference measure is given by a Bessel random walk, we derive the scaling limit of the annealed free energy as beta, h down arrow 0 in three different regimes for the tail exponent of phi.