有限型平均场模型中的亚态：可见性，不可见性和对称性的随机恢复
Metastates in finite-type mean-field models: visibility, invisibility, and random restoration of symmetry
摘要：
我们考虑一类一般的无序平均场模型，其中自旋变量和无序变量都取100个值。为了研究相变制度中的尺寸依赖性，我们构建了描述找到接近纯无限体积状态的特定凸组合的大系统的概率的亚态。我们表明，在非简并假设下，只有纯态，与非随机概率权重，我们推导出明确的表达式在无序变量的相互作用和分布。我们提供了一个几何结构区分不可见的状态（具有零权重）从可见的。作为进一步的结果，我们表明，在恰好有两个纯态的情况下，即使模型没有明显的对称性，这两个纯态也必然具有相同的权重。
英文摘要：
We consider a general class of disordered mean-field models where both the spin variables and disorder variables take finitely many values. To investigate the size-dependence in the phase-transition regime we construct the metastate describing the probabilities to find a large system close to a particular convex combination of the pure infinite-volume states. We show that, under a non-degeneracy assumption, only pure states are seen, with non-random probability weights for which we derive explicit expressions in terms of interactions and distributions of the disorder variables. We provide a geometric construction distinguishing invisible states (having zero weights) from visible ones. As a further consequence we show that, in the case where precisely two pure states are available, these must necessarily occur with the same weight, even if the model has no obvious symmetry relating the two.
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