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Exact properties of spin glasses. - I. 2D supersymmetry and Nishimori's result

We introduce an effective theory of interacting fermions and bosons in order to express the quenched internal energy of the 2D Ising spin glass. We show that an exact result derived by Nishimori appears, in this formulation, as a dimensional reduction due to the apparition of a supersymmetry. For a general Ising spin glass, this suggests new insights into the physical meaning of this exact result Proposition d'une theorie effective de fermions et bosons en interaction pour exprimer l'energie interne du verre de spin d'Ising 2D. Interpretation d'un resultat exact de Nishimori comme une reduction dimensionnelle due a l'apparition d'une supersymetrie