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Effets des fluctuations et invariance d'échelle locale dans les systèmes stochastiques hors-équilibre

Abstract : This thesis is devoted to the general area of ageing in ferromagnetic spin systems. Very remarkably, the physical properties of these materials can be organized in terms of a simple scaling picture and can be classified through some universal reference curves. Precisely, our study consists in rephrasing the problem of ageing in terms of the dynamical symmetries which caracterize this phenomena. On a theoretical point of view, we turn these invariances into a statistical field theory, through a systeamtic treatment of noisy effects, either of thermal type, or due to the preparation of the sample. In the framework of a Langevin stochastic differential equation with z=2, and for a ferromagnet which is Galilee-invariant without noise, we establish the two-point response function to be independent of the thermal fluctuations. Owing these hypothesis, we produce some analytic prediction of the form of the two-point correlation function when the system undergoes a phase-ordering dynamics at zero temperature. We test our results in some concrete situations. On a more descriptive point of view, we study some aspects of the ageing dynamics with quantifying the distance away from equilibrium. For exactly solvable models, we are interested in both the influence of the thermal history of the quench and the initial conditions on the long-time dynamics of the ferromagnet. We enlarge the validity of local-scale invariance to certain of these situations, and thus confirm the strength of this theory.
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Submitted on : Thursday, March 29, 2018 - 10:44:49 AM
Last modification on : Thursday, November 12, 2020 - 3:42:03 PM


  • HAL Id : tel-01746786, version 1



Alan Picone. Effets des fluctuations et invariance d'échelle locale dans les systèmes stochastiques hors-équilibre. Autre [cond-mat.other]. Université Henri Poincaré - Nancy 1, 2004. Français. ⟨NNT : 2004NAN10035⟩. ⟨tel-01746786⟩



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