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 be a continuous potential associated with a symbolic dynamical system over a finite alphabet. Introducing a parameter (interpreted as the inverse temperature) we study the regularity of the pressure function on an interval with . We say that ϕ has a phase transition at if the pressure function is not differentiable at . This is equivalent to the condition that the potential has two (ergodic) equilibrium states with distinct entropies. For any and any increasing sequence of real numbers contained in , we construct a potential ϕ whose phase transitions in occur precisely at the '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
让 是与符号动力学系统相关联的连续潜力 在有限的字母上。引入参数 (解释为逆温度),我们研究压力函数的规律性 每隔一段时间 和 。我们说ϕ在 如果压力功能 在 。这相当于潜在的条件具有两个(遍历)平衡态,具有不同的熵。对于任何 以及任何递增的实数序列 包含在 ,我们构建了一个潜在的φ,其相变的 恰好发生在 的。尤其是,我们获得的电势具有无限多的相变集。