On supersymmetry breaking in the computation of the complexity
On supersymmetry breaking in the computation of the complexity
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复杂度计算中的超对称破缺
DOI：
10.1088/0305-4470/37/33/001
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发表时间：
2004
期刊：
影响因子：
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通讯作者：
T. Rizzo
中科院分区：
文献类型：
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作者：
G. Parisi;T. Rizzo
本文研究了Thouless-Anderson-Palmer方程解的个数计算中超对称破缺的后果。我们表明，Kurchan的论点，证明了消失的前因子的布雷和摩尔鞍点的解决方案的总数可以扩展到解决方案在任何给定的自由能。我们还提供了一个新的简单的参数为消失的前因子，并使用它来证明孤立的本征值最近考虑Aspelmeier，Bray和摩尔在BM理论正是零，因为超对称破缺。孤立本征值的本征向量的行为也被认为是在较低的频带边缘。
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.