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Rigorous decimation-based construction of ground pure states for spin glass models on random lattices

S. Cocco·O. Dubois·J. Mandler·R. Monasson
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Abstract

A constructive scheme for determining pure states (clusters) 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 an exact decimation procedure. When the number c of couplings per spin is smaller than some critical value c_d, all spins are eliminated at the end of decimation (RS phase). In the range c_d<c<c_s, a reduced Hamiltonian is left; each ground state (GS) of the latter is a "seed" from which a cluster of GS of the original Hamiltonian can be reconstructed. Above c_s, GS are frustrated with an energy per spin larger than -c. The number of GS in each cluster, the number of clusters, the distances between GS are calculated and correspond to RSB predictions.

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S. Cocco, O. Dubois, J. Mandler, R. Monasson. 2002-07-18. Rigorous decimation-based construction of ground pure states for spin glass models on random lattices. https://doi.org/10.1103/physrevlett.90.047205

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