自旋玻璃计算与Ruelle几率级联
Spin Glass Computations and Ruelle's Probability Cascades
摘要：
我们研究的Parisi功能，出现在Parisi公式的SK模型的压力，作为一个功能的Ruelle的概率级联（RPC）。计算技术的RPC制定的功能。它们被用来获得连续性和单调性的功能检索Guerra定理。本文还详细讨论了Aizenman-Sims-Starr变分原理与Parisi公式之间的联系。作为技术的最后一个应用，我们重新派生的Almeida无齿线的精神Toninelli，但依赖于RPC结构。
英文摘要：
We study the Parisi functional, appearing in the Parisi formula for the pressure of the SK model, as a functional on Ruelle's Probability Cascades (RPC). Computation techniques for the RPC formulation of the functional are developed. They are used to derive continuity and monotonicity properties of the functional retrieving a theorem of Guerra. We also detail the connection between the Aizenman-Sims-Starr variational principle and the Parisi formula. As a final application of the techniques, we rederive the Almeida-Thouless line in the spirit of Toninelli but relying on the RPC structure.
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