2005/02/01 by Erwin Bolthausen, Giambattista Giacomin · 1 citation
Materials Science · Mathematics · Physics and Astronomy · #Markov Chains and Monte Carlo Methods #Material Dynamics and Properties #Theoretical and Computational Physics #math.PR #msc:60F10 #msc:60K35 #msc:82B41.
paper · pdf · doi:10.1214/105051604000000800
published as Annals of Applied Probability 2005, Vol. 15, No. 1B, 963-983 · Published at http://dx.doi.org/10.1214/105051604000000800 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org)
openalex publication_date 2005/02/01 · arxiv created 2005/03/24 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We analyze a (1+1)-dimension directed random walk model of a polymer dipped in a medium constituted by two immiscible solvents separated by a flat interface. The polymer chain is heterogeneous in the sense that a single monomer may energetically favor one or the other solvent. We focus on the case in which the polymer types are periodically distributed along the chain or, in other words, the polymer is constituted of identical stretches of fixed length. The phenomenon that one wants to analyze is the localization at the interface: energetically favored configurations place most of the monomers in the preferred solvent and this can be done only if the polymer sticks close to the interface. We investigate, by means of large deviations, the energy–entropy competition that may lead, according to the value of the parameters (the strength of the coupling between monomers and solvents and an asymmetry parameter), to localization. We express the free energy of the system in terms of a variational formula that we can solve. We then use the result to analyze the phase diagram.