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Smoothing effect of quenched disorder on polymer depinning transitions
- Source :
- Communications in Mathematical Physics, Communications in Mathematical Physics, Springer Verlag, 2006, 266 n.1, pp.1-16, Communications in Mathematical Physics, 2006, 266 n.1, pp.1-16
- Publication Year :
- 2006
- Publisher :
- HAL CCSD, 2006.
-
Abstract
- We consider general disordered models of pinning of directed polymers on a defect line. This class contains in particular the $(1+1)$--dimensional interface wetting model, the disordered Poland--Scheraga model of DNA denaturation and other $(1+d)$--dimensional polymers in interaction with flat interfaces. We consider also the case of copolymers with adsorption at a selective interface. Under quite general conditions, these models are known to have a (de)localization transition at some critical line in the phase diagram. In this work we prove in particular that, as soon as disorder is present, the transition is at least of second order, in the sense that the free energy is differentiable at the critical line, so that the order parameter vanishes continuously at the transition. On the other hand, it is known that the corresponding non--disordered models can have a first order (de)localization transition, with a discontinuous first derivative. Our result shows therefore that the presence of the disorder has really a smoothing effect on the transition. The relation with the predictions based on the Harris criterion is discussed.<br />Comment: 16 pages, 1 figure. v3: proof of the main theorem simplified, typos corrected, 1 reference added. To appear on Commun. Math. Phys
- Subjects :
- Work (thermodynamics)
[MATH.MATH-PR] Mathematics [math]/Probability [math.PR]
FOS: Physical sciences
01 natural sciences
010104 statistics & probability
Critical line
[PHYS.COND.CM-GEN] Physics [physics]/Condensed Matter [cond-mat]/Other [cond-mat.other]
[MATH.MATH-ST]Mathematics [math]/Statistics [math.ST]
FOS: Mathematics
Differentiable function
0101 mathematics
[MATH.MATH-ST] Mathematics [math]/Statistics [math.ST]
Mathematical Physics
Line (formation)
Phase diagram
Mathematics
chemistry.chemical_classification
Quantitative Biology::Biomolecules
Condensed matter physics
010102 general mathematics
Probability (math.PR)
Statistical and Nonlinear Physics
Polymer
Disordered Systems and Neural Networks (cond-mat.dis-nn)
Condensed Matter - Disordered Systems and Neural Networks
3. Good health
[MATH.MATH-PR]Mathematics [math]/Probability [math.PR]
chemistry
[PHYS.COND.CM-GEN]Physics [physics]/Condensed Matter [cond-mat]/Other [cond-mat.other]
Wetting
Mathematics - Probability
Smoothing
Subjects
Details
- Language :
- English
- ISSN :
- 00103616 and 14320916
- Database :
- OpenAIRE
- Journal :
- Communications in Mathematical Physics, Communications in Mathematical Physics, Springer Verlag, 2006, 266 n.1, pp.1-16, Communications in Mathematical Physics, 2006, 266 n.1, pp.1-16
- Accession number :
- edsair.doi.dedup.....86b0d617fd3ed334f2d84259e3dff7df