On Supersymmetry Breaking in the Computation of the Complexity

Details On Supersymmetry Breaking in the Computation of the Complexity On Supersymmetry Breaking in the Computation of the Complexity

2004-01-26

arxiv.org/abs/cond-mat/0401509v1

Physics

Condensed Matter

Disordered Systems and Neural Networks

12 pages

Scientific paper

10.1088/0305-4470/37/33/001

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.

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