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EQUALITY OF CRITICAL POINTS FOR POLYMER DEPINNING TRANSITIONS WITH LOOP EXPONENT ONE (811)
| Citations: | 18 - 2 self |
BibTeX
@MISC{Alexander811equalityof,
author = {Kenneth S. Alexander and Nikos Zygouras},
title = {EQUALITY OF CRITICAL POINTS FOR POLYMER DEPINNING TRANSITIONS WITH LOOP EXPONENT ONE},
year = {811}
}
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Abstract
Abstract. We consider a polymer with configuration modeled 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. 1.
