平均场铁磁体的稀释鲁棒性
Dilution Robustness for Mean Field Ferromagnets
摘要：
在这项工作中，我们比较了两种不同的随机稀释的平均场铁磁体：第一个模型是建立在伯努利稀释网络，而第二个生活在泊松稀释网络。虽然它是已知的，这两个模型在热力学极限相同的自由能，我们调查的结构约束，这两个模型必须履行。我们严格推导出每个模型的一组身份的多重叠分布使用不同的方法为两个稀释：在前一个模型中的约束是通过研究的后果的自平均的内部能量内能密度，而在后者是通过随机稳定性技术。最后，我们证明了两个模型中出现的身份是相同的，表明稀释网络的铁磁性质相对于稀释细节的“鲁棒性”。
英文摘要：
In this work we compare two different random dilution of a mean field ferromagnet: the first model is built on a Bernoulli-diluted network while the second lives on a Poisson-diluted network. While it is known that the two models have in the thermodynamic limit the same free energy we investigate on the structural constraints that the two models must fulfill. We rigorously derive for each model the set of identities for the multi-overlaps distribution using different methods for the two dilutions: constraints in the former model are obtained by studying the consequences of the self-averaging of the internal energy density, while in the latter are obtained by a stochastic-stability technique. Finally we prove that the identities emerging in the two models are the same, showing "robustness" of the ferromagnetic properties of diluted networks with respect to the details of dilution.
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