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Diagramme de phase du modele de Potts bidimensionnel.

Abstract : The Potts model describes the behaviour of ferromagnetics, by modelizing them as interacting spins with a number Q of states, located on a lattice. It is linked to many well-known problems in statistical physics and mathematics, as for example percolation or lattice colouring. In this thesis, we restrict ourselves to the case of a two-dimensional lattice, so we can use results of conformal invariance when the system is critical. In order to study its phase diagram, we decompose the partition function into characters for different boundary conditions, using the theory of representation of the quantum group Uq(sl(2)) and combinatorial methods. Then we determine numerically the limiting zeroes of the partition function in the complex temperature plane, and we conjecture properties of the phase diagram. In particular we show that the Berker-Kadanoff phase is not present when Q is equal to a Beraha number, and that new fixed points emerge.
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https://tel.archives-ouvertes.fr/tel-00097091
Contributor : Jean-Francois Richard <>
Submitted on : Wednesday, September 20, 2006 - 10:42:28 PM
Last modification on : Friday, May 29, 2020 - 4:01:47 PM
Long-term archiving on: : Friday, November 25, 2016 - 11:49:29 AM

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  • HAL Id : tel-00097091, version 1

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Jean-Francois Richard. Diagramme de phase du modele de Potts bidimensionnel.. Physique mathématique [math-ph]. Université Pierre et Marie Curie - Paris VI, 2006. Français. ⟨tel-00097091⟩

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