The rounding of the phase transition for disordered pinning with stretched exponential tails
Lacoin, Hubert (2017), The rounding of the phase transition for disordered pinning with stretched exponential tails, The Annals of Applied Probability, 27, 2, p. 917-943. 10.1214/16-AAP1220
TypeArticle accepté pour publication ou publié
External document linkhttps://arxiv.org/abs/1405.6875v3
Journal nameThe Annals of Applied Probability
Institute of Mathematical Statistics
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Abstract (EN)The presence of frozen-in or quenched disorder in a system can often modifythe nature of its phase transition. A particular instance ofthis phenomenon is the so-called rounding effect: it has been shown in many cases that the free-energy curve ofthe disordered system at its critical point is smoother thanthat of the homogenousone. In particular some disordered systems do not allow first-order transitions. Westudy this phenomenon for the pinning of a renewal with stretched-exponential tails on adefect line (the distributionKof the renewal increments satisfiesK(n)∼cKexp(−nα),α∈(0,1)) which has a first order transition when disorder is not present. We showthat the critical behavior of the disordered system dependson the value ofα: whenα >1/2 the transition remains first order, whereas the free-energy diagram is smoothedforα≤1/2. Furthermore we show that the rounding effect is getting stronger whenαdiminishes.
Subjects / KeywordsPhase transition; Harris Criterion; Rounding effect; Disordered pinning
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