Topological aspects of a long-range model |
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Institution: | 1. LEM3, Laboratoire d''Etude des Microstructures et de Mécanique des Matériaux, CNRS UMR 7239, Université de Lorraine, Ile du Saulcy, 57045 Metz, France;2. Laboratoire de mécanique Biomécanique, Polymère, Structures, EA 4632, Ecole Nationale d''Ingénieurs de Metz (ENIM), F-57012 Metz Cedex 01, France |
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Abstract: | The mean field XY Hamiltonian, a suitable model for studying long-range interactions in extended systems, presents, amongst other interesting features, slow relaxation and formation of quasi-stationary (QS) states. It is now known that, along these QS trajectories, the system visits critical points (maxima) of the potential energy function, characterized by a large number of directions with marginal stability. This observation may provide an interpretation for the slow relaxation dynamics and the trapping in such trajectories. In this paper we present further results and discussion on topological aspects of the model. |
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