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Multiple phase transitions on compact symbolic systems
Advances in Mathematics ( IF 1.7 ) Pub Date : 2021-05-10 , DOI: 10.1016/j.aim.2021.107768
Tamara Kucherenko , Anthony Quas , Christian Wolf

Let ϕ:XR be a continuous potential associated with a symbolic dynamical system T:XX over a finite alphabet. Introducing a parameter β>0 (interpreted as the inverse temperature) we study the regularity of the pressure function βPtop(βϕ) on an interval [α,) with α>0. We say that ϕ has a phase transition at β0 if the pressure function Ptop(βϕ) is not differentiable at β0. This is equivalent to the condition that the potential β0ϕ has two (ergodic) equilibrium states with distinct entropies. For any α>0 and any increasing sequence of real numbers (βn) contained in [α,), we construct a potential ϕ whose phase transitions in [α,) occur precisely at the βn's. In particular, we obtain a potential which has a countably infinite set of phase transitions.



中文翻译:

紧凑符号系统上的多相变

ϕX[R 是与符号动力学系统相关联的连续潜力 ŤXX在有限的字母上。引入参数β>0 (解释为逆温度),我们研究压力函数的规律性 βP最佳βϕ 每隔一段时间 [αα>0。我们说ϕβ0 如果压力功能 P最佳βϕβ0。这相当于潜在的条件β0ϕ具有两个(遍历)平衡态,具有不同的熵。对于任何α>0 以及任何递增的实数序列 βñ 包含在 [α,我们构建了一个潜在的φ,其相变的[α 恰好发生在 βñ的。尤其是,我们获得的电势具有无限多的相变集。

更新日期:2021-05-11
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