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Unbinding of mutually avoiding random walks and two dimensional quantum gravity

Enrico Carlon·Marco Baiesi
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Abstract

We analyze the unbinding transition for a two dimensional lattice polymer in which the constituent strands are mutually avoiding random walks. At low temperatures the strands are bound and form a single self-avoiding walk. We show that unbinding in this model is a strong first order transition. The entropic exponents associated to denaturated loops and end-segments distributions show sharp differences at the transition point and in the high temperature phase. Their values can be deduced from some exact arguments relying on a conformal mapping of copolymer networks into a fluctuating geometry, i.e. in the presence of quantum gravity. An excellent agreement between analytical and numerical estimates is observed for all cases analized.

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Enrico Carlon, Marco Baiesi. 2004-05-10. Unbinding of mutually avoiding random walks and two dimensional quantum gravity. https://doi.org/10.1103/physreve.70.066118

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