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April 2017 The rounding of the phase transition for disordered pinning with stretched exponential tails
Hubert Lacoin
Ann. Appl. Probab. 27(2): 917-943 (April 2017). DOI: 10.1214/16-AAP1220

Abstract

The presence of frozen-in or quenched disorder in a system can often modify the nature of its phase transition. A particular instance of this phenomenon is the so-called rounding effect: it has been shown in many cases that the free energy curve of the disordered system at its critical point is smoother than that of the homogeneous one. In particular some disordered systems do not allow first-order transitions. We study this phenomenon for the pinning of a renewal with stretched-exponential tails on a defect line (the distribution $K$ of the renewal increments satisfies $K(n)\sim c_{K}\exp(-n^{\zeta})$, $\zeta\in(0,1)$) which has a first order transition when disorder is not present. We show that the critical behavior of the disordered system depends on the value of $\zeta$: when $\zeta>1/2$ the transition remains of first order, whereas the free energy diagram is smoothed for $\zeta\le1/2$. Furthermore we show that the rounding effect is getting stronger when $\zeta$ diminishes.

Citation

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Hubert Lacoin. "The rounding of the phase transition for disordered pinning with stretched exponential tails." Ann. Appl. Probab. 27 (2) 917 - 943, April 2017. https://doi.org/10.1214/16-AAP1220

Information

Received: 1 October 2015; Published: April 2017
First available in Project Euclid: 26 May 2017

zbMATH: 1370.60190
MathSciNet: MR3655857
Digital Object Identifier: 10.1214/16-AAP1220

Subjects:
Primary: 60K35, 60K37, 82B27, 82B44

Rights: Copyright © 2017 Institute of Mathematical Statistics

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Vol.27 • No. 2 • April 2017
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