摘要翻译：
我们研究了铁磁体的平均场稀释模型。我们找到并证明了在高温和零温度下自由能密度的表达式。我们找到了模型的临界线，将磁化强度为零的相和对称性破缺的相分开。我们还精确地计算了零温度下的熵，它严格为正。零温度下的物理行为是非常有趣的，与无限维渗流有关，并暗示了一般低温下的可能行为。最后给出了退火模型的完整解。我们的结果对泊松和伯努利模型都成立。
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英文标题：
《Mean field dilute ferromagnet I. High temperature and zero temperature
  behavior》
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作者：
Luca De Sanctis, Francesco Guerra
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最新提交年份：
2008
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分类信息：

一级分类：Physics        物理学
二级分类：Statistical Mechanics        统计力学
分类描述：Phase transitions, thermodynamics, field theory, non-equilibrium phenomena, renormalization group and scaling, integrable models, turbulence
相变，热力学，场论，非平衡现象，重整化群和标度，可积模型，湍流
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一级分类：Physics        物理学
二级分类：Disordered Systems and Neural Networks        无序系统与神经网络
分类描述：Glasses and spin glasses; properties of random, aperiodic and quasiperiodic systems; transport in disordered media; localization; phenomena mediated by defects and disorder; neural networks
眼镜和旋转眼镜；随机、非周期和准周期系统的性质；无序介质中的传输；本地化；由缺陷和无序介导的现象；神经网络
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英文摘要：
  We study the mean field dilute model of a ferromagnet. We find and prove an expression for the free energy density at high temperature, and at temperature zero. We find the critical line of the model, separating the phase with zero magnetization from the phase with symmetry breaking. We also compute exactly the entropy at temperature zero, which is strictly positive. The physical behavior at temperature zero is very interesting and related to infinite dimensional percolation, and suggests possible behaviors at generic low temperatures. Lastly, we provide a complete solution for the annealed model. Our results hold both for the Poisson and the Bernoulli versions of the model.
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PDF链接：
https://arxiv.org/pdf/801.494