Rigorous decimation-based construction of ground pure states for spin-glass models on random lattices.
A constructive scheme for determining pure states at very low temperature in the 3-spins glass model on a random lattice is provided, in full agreement with Parisi's one step replica symmetry breaking (RSB) scheme. Proof is based on the analysis of a partial decimation procedure and of the statistical properties of its output, i.e., a reduced Hamiltonian acting on a subset of the initial spins. The number of ground states (GS) in each state, the number of states, and the distances between GS are calculated and correspond to RSB predictions.
Cocco
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S
CNRS-Laboratoire de Dynamique des Fluides Complexes, 3 Rue de l'Université, 67000 Strasbourg, France.
Dubois
O
O
Mandler
J
J
Monasson
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R