论文标题
无限体积的吉布斯状态和随机场平均球形模型的转移
Infinite volume Gibbs states and metastates of the random field mean-field spherical model
论文作者
论文摘要
对于离散的随机场Curie-Weiss模型，已经研究并确定了无限体积的Gibbs状态和转移物，并确定了随机外部场的特定实例。通常，对于离散或连续自旋系统的非平凡限制转移物的文献中，没有很多例子。我们在一般的随机外部场中分析了平均场球形模型的无限体积GibbS状态，一种连续自旋的模型，具有独立的分布分布的组件，其有限的矩具有大于四个和非散落差异的有限阶段。根据模型的参数，我们表明存在三个不同的阶段：有序的铁磁，有序的顺磁性和自旋玻璃。在有序的铁磁和有序的顺磁性阶段中，我们表明，几乎肯定存在独特的无限体积吉布斯状态。在自旋玻璃相中，我们显示了混乱的尺寸依赖性的存在，提供了Aizenman-Wehr转移物的构造，并考虑分布的收敛性和几乎确定的Newman-Stein转移的收敛性。限制转移是非平凡的，由于高斯波动和球形约束，它们的结构是普遍的。
For the discrete random field Curie-Weiss models, the infinite volume Gibbs states and metastates have been investigated and determined for specific instances of random external fields. In general, there are not many examples in the literature of non-trivial limiting metastates for discrete or continuous spin systems. We analyze the infinite volume Gibbs states of the mean-field spherical model, a model of continuous spins, in a general random external field with independent identically distributed components with finite moments of some order larger than four and non-vanishing variances of the second moments. Depending on the parameters of the model, we show that there exist three distinct phases: ordered ferromagnetic, ordered paramagnetic, and spin glass. In the ordered ferromagnetic and ordered paramagnetic phases, we show that there exists a unique infinite volume Gibbs state almost surely. In the spin glass phase, we show the existence of chaotic size dependence, provide a construction of the Aizenman-Wehr metastate, and consider both the convergence in distribution and almost sure convergence of the Newman-Stein metastates. The limiting metastates are non-trivial and their structure is universal due to the presence of Gaussian fluctuations and the spherical constraint.
