论文标题
广义的居里 - 韦斯 - 波特模型和二次压力中
Generalized Curie-Weiss-Potts model and quadratic pressure in ergodic theory
论文作者
论文摘要
我们将吉布斯（Gibbs）系列的二次压力和收敛性扩展到从作者的先前加入的工作到居里 - 韦斯 - 彼得斯模型的结果。我们为二次压力定义了平衡状态的概念，并表明在某些辅助功能的最大值的某些条件下，Gibbs测量将转移操作员的特征测量的凸组合收敛到凸组合。该扩展程序适用于{Infinite-to-One}地图定义的动态系统。例如，我们计算{均值场} $ xy $模型的平衡，因为粒子数量为$+\ infty $。
We extend results on quadratic pressure and convergence of Gibbs mesures from previous joined work of the authors to the Curie-Weiss-Potts model. We define the notion of equilibrium state for the quadratic pressure and show that under some conditions on the maxima for some auxiliary function, the Gibbs measure converges to a convex combination of eigen-measures for the Transfer Operator. This extension works for dynamical systems defined by {infinite-to-one} maps. As an example, we compute the equilibrium for {the mean-field} $XY$ model as the number of particles goes to $+\infty$.
