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Statut |
Confirmé |
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Série |
SOUTEN-TH |
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Domaines |
hep-ph |
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Date |
Mercredi 13 Décembre 2017 |
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Heure |
14:00 |
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Institut |
LPT |
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Salle |
Amphi 1, bat 210, 2eme etage, LPT Orsay |
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Nom de l'orateur |
Salazar |
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Prenom de l'orateur |
Robert |
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Addresse email de l'orateur |
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Institution de l'orateur |
LPT Orsay/Universidad Los Andes (Colombie) |
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Titre |
Exact results and melting mechanisms for two-dimensional systems |
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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 short-range interactions
and continuous degrees of freedom do not have long-range 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 Kosterlitz-Thouless (KT)-transition for the XY -model showing that
transitions may take place in positional isotropic bidimensional systems if they still have quasi-long 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, two-dimensional 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 Kosterlitz-Thouless-Halperin-Nelson-Young (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 two-dimensional 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 multi-histogram method.
Finally, a statistical analysis of clusters of defects during melting conrms in a detailed way the predictions
of the KTHNY-theory but also provides alternatives to detect transitions in two-dimensional systems.
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Numéro de preprint arXiv |
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