论文标题
大偏差和块旋转Potts模型中的相变
Large deviations and a phase transition in the Block Spin Potts models
论文作者
论文摘要
我们介绍和分析了跨界文章中讨论的跨度Ising（Curie-Weiss）模型的概括。在这些块旋转模型中，每种旋转$ s $块中的一个旋转可以采用$ q \ ge 3 $值的有限数之一，因此名称block spin potts型号。旋转可以采取的值称为颜色。我们证明了在特定块中某种颜色的旋转百分比的较大偏差原理。这些值以$ s \ times q $矩阵表示。我们表明，对于均匀的块大小和适当选择的相互作用强度，有相变。在某些制度中，唯一的平衡是所有块中所有颜色的均匀分布，而在其他参数方面，有一种主要的颜色，而对于所有块，这是相同的颜色，频率相同。最后，我们为Block Spin Potts模型建立了对数 - 贝贝型型不等式。
We introduce and analyze a generalization of the blocks spin Ising (Curie-Weiss) models that were discussed in a number of recent articles. In these block spin models each spin in one of $s$ blocks can take one of a finite number of $q \ge 3$ values, hence the name block spin Potts model. The values a spin can take are called colors. We prove a large deviation principle for the percentage of spins of a certain color in a certain block. These values are represented in an $s \times q$ matrix. We show that for uniform block sizes and appropriately chosen interaction strength there is a phase transition. In some regime the only equilibrium is the uniform distribution of all colors in all blocks, while in other parameter regimes there is one predominant color, and this is the same color with the same frequency for all blocks. Finally, we establish log-Sobolev-type inequalities for the block spin Potts model.
