A copolymer near a selective interface: variational characterization of the free energy
| Autor: | Alex Opoku, Erwin Bolthausen, den WThF Frank Hollander |
|---|---|
| Přispěvatelé: | Eurandom |
| Jazyk: | angličtina |
| Rok vydání: | 2015 |
| Předmět: |
Statistics and Probability
Phase transition 82B44 FOS: Physical sciences Thermodynamics selective interface large deviation principle localization vs delocalization critical curve Power law variational formula Combinatorics chemistry.chemical_compound symbols.namesake Delocalized electron Copolymer FOS: Mathematics 60F10 60K37 82B27 Mathematical Physics Mathematics Probability (math.PR) Mathematical Physics (math-ph) free energy Condensed Matter::Soft Condensed Matter 60K37 Monomer chemistry specific relative entropy symbols Exponent Statistics Probability and Uncertainty Hamiltonian (quantum mechanics) Rate function Mathematics - Probability 60F10 82B27 |
| Zdroj: | Annals of Probability The Annals of Probability Annals of Probability, 43(2), 875-933 Ann. Probab. 43, no. 2 (2015), 875-933 |
| Popis: | In this paper we consider a two-dimensional copolymer consisting of a random concatenation of hydrophobic and hydrophilic monomers near a linear interface separating oil and water acting as solvents. The configurations of the copolymer are directed paths that can move above and below the interface. The interaction Hamiltonian, which rewards matches and penalizes mismatches of the monomers and the solvents, depends on two parameters: the interaction strength $\beta\geq 0$ and the interaction bias $h \geq 0$. The quenched excess free energy per monomer $(\beta,h) \mapsto g^\mathrm{que} (\beta,h)$ has a phase transition along a quenched critical curve $\beta \mapsto h^\mathrm{que}_c(\beta)$ separating a localized phase, where the copolymer stays close to the interface, from a delocalized phase, where the copolymer wanders away from the interface. We derive a variational expression for $g^\mathrm{que}(\beta,h)$ by applying the quenched large deviation principle for the empirical process of words cut out from a random letter sequence according to a random renewal process. We compare this variational expression with its annealed analogue, describing the annealed excess free energy $(\beta,h) \mapsto g^\mathrm{ann}(\beta,h)$, which has a phase transition along an annealed critical curve $\beta \mapsto h^\mathrm{ann}_c(\beta)$. Our results extend to a general class of disorder distributions and directed paths. We show that $g^\mathrm{que}(\beta,h)0$ when $\alpha>1$. This gap vanished when $\alpha=1$. Comment: 39 pages, 8 figures |
| Databáze: | OpenAIRE |
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