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Energy landscape in three-dimensional Heisenberg spin glasses

Recent work suggests that Heisenberg spin glasses may belong to the same universality class than structural glasses. Indeed, finding a lattice equivalent for supercooled liquids would probably allow easier numerical and analytical studies, that may help to answer long-standing questions on the glass transition. Supercooled liquids have many peculiar behaviors that should be found in the paramagnetic phase of Heisenberg spin glasses if the analogy between the two systems holds. It is with this motivation that we undertake a study of the paramagnetic phase of Heisenberg spin glasses. We shall emphasize the role of the energy landscape, with a detailed study of the properties of the inherent structures (by analogy with supercooled liquids, we name inherent structure the local minimum of the energy function which is closest to the current spin configuration). Finding inherent structures will require the development of a new search algorithm. We shall investigate as well the existence of a dynamic transition in the paramagnetic phase. As a matter of fact, both the existence of a complex energy landscape, as well as the existence of a dynamic transition, are distinguished features of the Physics of supercooled liquids.