A variational formula for the free energy of the partially directed polymer collapse

Abstract

Long linear polymers in dilute solutions are known to undergo a collapse transition from a random coil (expand itself) to a compact ball (fold itself up) when the temperature is lowered, or the solvent quality deteriorates. A natural model for this phenomenon is a 1+1 dimensional self-interacting and partially directed self-avoiding walk. In this paper, we develop a new method to study the partition function of this model, from which we derive a variational formula for the free energy. This variational formula allows us to prove the existence of the collapse transition and to identify the critical temperature in a simple way. We also prove that the order of the collapse transition is 3/2.

18 pages, 5 figures

References in corpus (2)

• Pinning and wetting transition for (1+1)-dimensional fields with Laplacian interaction
• Families of prudent self-avoiding walks

Cited by in corpus (5)

• Analysis of series expansions for non-algebraic singularities
• Interacting partially directed self-avoiding walk: a probabilistic perspective
• Adsorption of symmetric random copolymer onto symmetric random surface: the annealed case
• Interacting Elastic Lattice Polymers: a Study of the Free-Energy of Globular Rings
• A sharp asymptotics of the partition function for the collapsed interacting partially directed self-avoiding walk