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Theses

Role of fluctuations in finite-dimensional glassy systems

Abstract : When the temperature diminishes, glassy systems present a very sluggish dynamics and at low enough temperature can finish in some arrested disordered state. This thesis deals about the case of structural glasses, to which category supercooled liquids belong to, and spin glasses.In these two cases the physical scenarios issued from the mean-field theories are known and could be fragile to the introduction of fluctuations that are present in finite-dimensional systems. Since the study of the effect of fluctuations in glassy systems is a daunting task, the aim of this thesis is to study simple related problems in which the effect of fluctuations can be thoroughly investigated.For the structural-glass case, we study first the return to convexity of the free energy of a uni-dimensional finite-size system where fluctuations are restricted by the finite size of the system. Then, we study the role of "short"- and "long"-range fluctuations in a glass-former model called ``plaquette model'' in comparing the thermodynamic properties of the system which are known on Euclidean lattices with the ones we obtained on a "tree" lattice. Finally, we study the existence of space-time fluctuations in a model made of activated-dynamics systems coupled via a thermal bath at low temperature.For the spin-glass case, we construct a scheme for the nonperturbative renormalization group to describe the effect of critical fluctuations on the critical properties of the Ising spin glass in zero field in dimensions lower than six.
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Charlotte Rulquin. Role of fluctuations in finite-dimensional glassy systems. Condensed Matter [cond-mat]. Université Pierre et Marie Curie - Paris VI, 2017. English. ⟨NNT : 2017PA066454⟩. ⟨tel-01786991⟩

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