Open Access
February 2010 Equality of critical points for polymer depinning transitions with loop exponent one
Kenneth S. Alexander, Nikos Zygouras
Ann. Appl. Probab. 20(1): 356-366 (February 2010). DOI: 10.1214/09-AAP621

Abstract

We consider a polymer with configuration modelled by the trajectory of a Markov chain, interacting with a potential of form u+Vn when it visits a particular state 0 at time n, with {Vn} representing i.i.d. quenched disorder. There is a critical value of u above which the polymer is pinned by the potential. A particular case not covered in a number of previous studies is that of loop exponent one, in which the probability of an excursion of length n takes the form φ(n)/n for some slowly varying φ; this includes simple random walk in two dimensions. We show that in this case, at all temperatures, the critical values of u in the quenched and annealed models are equal, in contrast to all other loop exponents, for which these critical values are known to differ, at least at low temperatures.

Citation

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Kenneth S. Alexander. Nikos Zygouras. "Equality of critical points for polymer depinning transitions with loop exponent one." Ann. Appl. Probab. 20 (1) 356 - 366, February 2010. https://doi.org/10.1214/09-AAP621

Information

Published: February 2010
First available in Project Euclid: 8 January 2010

zbMATH: 1187.82054
MathSciNet: MR2582651
Digital Object Identifier: 10.1214/09-AAP621

Subjects:
Primary: 82B44
Secondary: 60K35 , 82D60

Keywords: Disorder , Pinning , Polymer , quenched critical point , Random potential

Rights: Copyright © 2010 Institute of Mathematical Statistics

Vol.20 • No. 1 • February 2010
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