Polymers in random environment : influence of correlated disorder on the localization phenomenon

Abstract : This thesis studies models of polymers in random environment: we focus on the case of a directed polymer in dimension d+1 that interacts with a one-dimensional defect. The interactions are possibly inhomogeneous, and are represented by random variables. We deal with the question of the influence of disorder on the localization phenomenon: we want to determine if the presence of inhomogeneities modifies the critical properties of the system, and especially the characteristics of the phase transition (in that case disorder is said to be pertinent). In particular, we prove that if the defect is a random walk, disorder is relevant in dimension d≥3. We then study the pinning model in random correlated environment. There is a non-rigourous criterion (due to Weinrib and Halperin), that we can apply to our model, and that predicts disorder relevance/irrelevance, according to the value of the critical exponent of the homogeneous system, denoted νpur, and of the correlation decay exponent. When disorder is Gaussian and correlations are summable, we show that the Weinrib-Halperin criterion is valid: we prove this in the hierarchical version of the model, and also, partially, in the non-hierachical (standard) framework. Moreover, we obtained a surprising result: when correlations are sufficiently strong, and in particular when they are non-summable (in the gaussian framework), a new regime in which disorder is always relevant appears, the order of the phase transition being always larger than νpur. The Weinrib-Halperin prediction therefore does not apply to our model.
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Other [cond-mat.other]. Ecole normale supérieure de lyon - ENS LYON, 2012. English. <NNT : 2012ENSL0716>


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Quentin Berger. Polymers in random environment : influence of correlated disorder on the localization phenomenon. Other [cond-mat.other]. Ecole normale supérieure de lyon - ENS LYON, 2012. English. <NNT : 2012ENSL0716>. <tel-00726494>

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