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Etudes théoriques des transitions de phase dans des réseaux bidimensionnels périodiques de spins

Abstract : This thesis presents developments of methods devoted to the theoretical treatment of periodic spins lattices. One of them (Self-Consistent Perturbation) is inspired by perturbative expansion of the wave function from a very localized reference function. This variant of the Coupled Cluster formalism leads to easily solvable sets of coupled polynomial equations. The other methods are based on scale changes, in the spirit of the Real Space Renormalization Group, the lattice being seen as blocks in interaction. The theory of effective Hamiltonians, using the exact spectrum of the dimers or trimers allows one to define effective interactions. One may work with blocks involving odd number of sites, considered as quasi-spins, which may produce isomorphic lattices in an iterative scheme and keeps the concepts and elegance of the Renormalization Group, or blocks of even number of sites, that drives to a renormalized excitonic description of the excited states. The methods were tested on simple lattices, then applied to the research of phase transitions on a series of two-dimensional lattices (anisotropic square, 1/5-depleted, plaquette, Shastry-Sutherland) and ribbons of graphite. The locations of the phase transitions (and the values of the gaps) are consistently predicted by the various methods used and in good agreement with the best available evaluations. The suggestion of the existence of an intermediate phase in the Shastry-Sutherland lattice is reinforced by our computations.
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https://tel.archives-ouvertes.fr/tel-00011173
Contributor : Mohamad Al Hajj <>
Submitted on : Thursday, December 8, 2005 - 3:55:27 PM
Last modification on : Friday, February 28, 2020 - 1:57:33 PM
Long-term archiving on: : Friday, April 2, 2010 - 11:25:33 PM

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Mohamad Al Hajj. Etudes théoriques des transitions de phase dans des réseaux bidimensionnels périodiques de spins. Matière Condensée [cond-mat]. Université Paul Sabatier - Toulouse III, 2005. Français. ⟨tel-00011173⟩

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