On supersymmetry breaking in the computation of the complexity
Copyright policy )On supersymmetry breaking in the computation of the complexity
We study the consequences of supersymmetry breaking in the computation of the number of solutions of the Thouless-Anderson-Palmer (TAP) equations. We show that Kurchan argument that proves the vanishing of the prefactor of the Bray and Moore saddle point for the total number of solutions can be extended to solutions at any given free energy. We also provide a new simple argument for the vanishing of the prefactor and use it to prove that the isolated eigenvalue recently considered by Aspelmeier, Bray and Moore is exactly zero in the BM theory because of supersymmetry breaking. The behavior of the eigenvector of the isolated eigenvalue at the lower band edge is also considered.
12 pages
- Roma Tre University Italy
- Sapienza University of Rome Italy
FOS: Physical sciences, Disordered Systems and Neural Networks (cond-mat.dis-nn), Condensed Matter - Disordered Systems and Neural Networks, Disordered systems (random Ising models, random Schrödinger operators, etc.) in equilibrium statistical mechanics, Statistical mechanics of random media, disordered materials (including liquid crystals and spin glasses)
FOS: Physical sciences, Disordered Systems and Neural Networks (cond-mat.dis-nn), Condensed Matter - Disordered Systems and Neural Networks, Disordered systems (random Ising models, random Schrödinger operators, etc.) in equilibrium statistical mechanics, Statistical mechanics of random media, disordered materials (including liquid crystals and spin glasses)
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