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 the 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 behaviour of the eigenvector of the isolated eigenvalue at the lower-band edge is also considered.
On supersymmetry breaking in the computation of the complexity / Parisi, Giorgio; T., Rizzo. - In: JOURNAL OF PHYSICS. A, MATHEMATICAL AND GENERAL. - ISSN 0305-4470. - 37:33(2004), pp. 7979-7992. [10.1088/0305-4470/37/33/001]
On supersymmetry breaking in the computation of the complexity
PARISI, Giorgio;
2004
Abstract
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 the 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 behaviour of the eigenvector of the isolated eigenvalue at the lower-band edge is also considered.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
