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Transitions topologiques dans des systèmes bidimensionnels de symétrie continue

Abstract : The role of interaction and spin symmetries is studied in two-dimensional O(n) spin models which are likely to describe nematic-isotropic transitions in liquid crystals. Additionally the relevance of impurties in such systems is analysed. We first study the XY model in order to check the efficiency of our numerical methods (finite-size scaling, conformal mappings). Once optimized, the numerical techniques are applied to the Lebwohl-Lasher model. A topological transition is found and the correlation functioncritical exponent is in remarkable agreement with the spin-wave approximation at low temperature. Then, we study along the same lines an Abelian and a non-Abelian model with P4-type interactions. The Abelian model displays a BKT-like transition, where as the non-Abelian model displays a first order transition with quasi-long-range order at low temperature. Finaly, the influence of quenched disorder in the XY model is studied, confirming the irrelevance of randomness in accordance with Harris criterion. In the disordered non-Abelian model with P4 interaction, we determine the phase diagram.
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http://docnum.univ-lorraine.fr/prive/SCD_T_2004_0227_FARINAS_SANCHEZ.pdf
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Submitted on : Thursday, March 29, 2018 - 10:43:01 AM
Last modification on : Thursday, November 12, 2020 - 3:42:03 PM

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Isabel Fariñas Sànchez. Transitions topologiques dans des systèmes bidimensionnels de symétrie continue. Autre [cond-mat.other]. Université Henri Poincaré - Nancy 1, 2004. Français. ⟨NNT : 2004NAN10227⟩. ⟨tel-01746705⟩

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