Statut  Confirmé 
Série  SOUTENTH 
Domaines  hepph 
Date  Mercredi 13 Décembre 2017 
Heure  14:00 
Institut  LPT 
Salle  Amphi 1, bat 210, 2eme etage, LPT Orsay 
Nom de l'orateur  Salazar 
Prenom de l'orateur  Robert 
Addresse email de l'orateur  
Institution de l'orateur  LPT Orsay/Universidad Los Andes (Colombie) 
Titre  Exact results and melting mechanisms for twodimensional systems 
Résumé  Many particle systems may exhibit interesting properties depending on the interaction between their con stituents. Among them, it is possible to nd situations where highly ordered microscopic structures may emerge from these interactions. The central problem to identify the mechanisms which activate the ordered particle arrangements has been the subject matter of theoretical and experimental studies. In the past decades, it was rigorously proved that systems in two dimensions with suciently shortrange interactions and continuous degrees of freedom do not have longrange order. In contrast, numerical studies of systems featuring lack of positional order in two dimensions showed evidence of phase transitions. This apparent contradiction was explained by the KosterlitzThouless (KT)transition for the XY model showing that transitions may take place in positional isotropic bidimensional systems if they still have quasilong range (QLR) order. Such QLR order associated to the orientational order of the system, is lost when topological defects activated by thermal uctuations begin to unbind in pairs producing a transition. On the other hand, twodimensional systems with positional order at vanishing temperature may show a melting scenario including three phases solid/hexatic/ uid with transitions driven by a unbinding mechanism of topological defects according to the KosterlitzThoulessHalperinNelsonYoung (KTHNY)theory. This work is focused on the study of the two dimensional one component plasma 2dOCP a system of N identical punctual charges interacting with an electric potential in a twodimensional surface with neutralizing background. The system is a crystal at vanishing temperature and it melts at suciently high temperature. If the interaction potential is logarithmic, then the system on the at plane and the sphere is exactly solvable at a special temperature located at the uid phase. We use analytical approaches to compute exactly thermodynamic variables and structural properties which enables to study the crossover behaviour from a disordered phases to crystals for small systems nding interesting connections with the Ginibre Ensemble of the random matrix theory. We perform numerical Monte Carlo simulations of the 2dOCP with inverse power law interactions and periodic boundary conditions nding a hexatic phase for suciently large systems. It is found a weakly rst order transition for the hexatic/ uid transition by using nite size analysis and the multihistogram method. Finally, a statistical analysis of clusters of defects during melting conrms in a detailed way the predictions of the KTHNYtheory but also provides alternatives to detect transitions in twodimensional systems. 
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