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Stable and Metastable Phases for the Curie–Weiss–Potts Model in Vector-Valued Fields via Singularity Theory
Journal of Statistical Physics ( IF 1.6 ) Pub Date : 2020-08-01 , DOI: 10.1007/s10955-020-02615-y
Christof Külske , Daniel Meißner

We study the metastable minima of the Curie-Weiss Potts model with three states, as a function of the inverse temperature, and for arbitrary vector-valued external fields. Extending the classic work of Ellis/Wang and Wang we use singularity theory to provide the global structure of metastable (or local) minima. In particular, we show that the free energy has up to four local minimizers (some of which may at the same time be global) and describe the bifurcation geometry of their transitions under variation of the parameters.

中文翻译:

基于奇异性理论的向量值场中居里-魏斯-波茨模型的稳定和亚稳定相

我们研究了具有三个状态的居里-魏斯波茨模型的亚稳态最小值,作为逆温度的函数,以及任意矢量值外部场。扩展 Ellis/Wang 和 Wang 的经典工作,我们使用奇异理论来提供亚稳态(或局部)最小值的全局结构。特别是,我们表明自由能有多达四个局部极小值(其中一些可能同时是全局的),并描述了在参数变化下它们转变的分岔几何形状。
更新日期:2020-08-01
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