Statut  Confirmé 
Série  FORUMENS 
Domaines  condmat.statmech 
Date  Mercredi 24 Mai 2023 
Heure  14:00 
Institut  LPENS 
Salle  L378 
Nom de l'orateur  Mauri 
Prenom de l'orateur  Achille 
Addresse email de l'orateur  
Institution de l'orateur  Radboud University 
Titre  Statistical mechanics of elastic membranes in classical and quantum regimes 
Résumé  The structure of thermallyfluctuating freestanding membranes has been a subject of investigation for several decades and has attracted a renewed interest in connection with graphene and atomicallythin twodimensional materials. A crucial theoretical prediction is that solid membranes, in absence of applied stress, behave as scaleinvariant rough surfaces, with universal scaling properties controlled by an interacting renormalizationgroup (RG) fixed point. This presentation will address the relation between scale and conformal invariance at the corresponding fixed point. By an analysis within the epsilon expansion, it will be shown that the theory is not symmetric under special conformal transformations, and thus provides an example of a scaleinvariant but nonconformal field theory. The second part of the presentation will analyze the role of quantum mechanical effects on the low temperature behavior of freestanding membranes. By a powercounting analysis, it will be shown that the leading behavior can be described by an effective renormalizable model in which the kinetic energy of inplane phonons is neglected, alongside other 'irrelevant' terms. The resulting RG equations, combined with arguments of finitesize scaling, will be used to derive general scaling laws for correlation functions and thermodynamical quantities. The results confirm, in a systematic framework, some predictions of earlier investigations. Strictly at T=0, the bending rigidity and the elastic moduli are renormalized logarithmically. At small T, the scaling laws and an explicit analysis of thermal fluctuations corroborate a striking thermodynamical prediction: the thermal expansion coefficient vanishes for T>0 as a slow, logarithmic function of T. 
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