The Statistical Mechanics of Stretched Polymers

Abstract

We describe some recent results concerning the statistical properties of a self-interacting polymer stretched by an external force. We concentrate mainly on the cases of purely attractive or purely repulsive self-interactions, but our results are stable under suitable small perturbations of these pure cases. We provide in particular a precise description of the stretched phase (local limit theorems for the end-point and local observables, invariance principle, microscopic structure). Our results also characterize precisely the (non-trivial, direction-dependent) critical force needed to trigger the collapsed/stretched phase transition in the attractive case. We also describe some recent progress: first, the determination of the order of the phase transition in the attractive case; second, a proof that a semi-directed polymer in quenched random environment is diffusive in dimensions 4 and higher when the temperature is high enough. In addition, we correct an incomplete argument from one of our earlier works.

References in corpus (1)

• Coincidence of Lyapunov exponents for random walks in weak random potentials

Cited by in corpus (15)

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• Polygons in restricted geometries subjected to infinite forces
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• Force-induced desorption of $3$-star polymers: a self-avoiding walk model
• Structure of Gibbs measures for planar FK-percolation and Potts models
• Force-induced desorption of uniform block copolymers
• Lower Bounds on the Localisation Length of Balanced Random Quantum Walks
• Critical behaviour of the extended-ballistic transition for pulled self-avoiding walks
• Biased random walk conditioned on survival among Bernoulli obstacles: subcritical phase
• Compressed self-avoiding walks in two and three dimensions
• Ornstein-Zernike behavior for Ising models with infinite-range interactions