压力功能的灵活性
Flexibility of the Pressure Function
摘要：
我们研究的灵活性的压力函数的连续势（可观察）相对于一个参数视为逆温度。该函数的不可微点在统计物理学中特别有趣，因为它们对应于相变。众所周知，压力函数是凸的，Lipschitz，并且在无穷远处有一个渐近线。我们证明，在一维紧凑的符号系统的设置，这些是唯一的限制。我们提出了一种方法来明确地构造一个连续的潜力，其压力函数符合\emph{any}规定的凸Lipschitz渐近线性函数开始在一个给定的参数正值。事实上，我们建立了这个结果的多维版本。因此，我们得到，对于一个连续的可观察的相变可以发生在一个可数的密集的温度值。我们进一步表明，可以改变基数的遍历平衡态作为一个函数的参数是任何数量，有限或无限的。
英文摘要：
We study the flexibility of the pressure function of a continuous potential (observable) with respect to a parameter regarded as the inverse temperature. The points of non-differentiability of this function are of particular interest in statistical physics, since they correspond to phase transitions. It is well known that the pressure function is convex, Lipschitz, and has an asymptote at infinity. We prove that in a setting of one-dimensional compact symbolic systems these are the only restrictions. We present a method to explicitly construct a continuous potential whose pressure function coincides with \emph{any} prescribed convex Lipschitz asymptotically linear function starting at a given positive value of the parameter. In fact, we establish a multidimensional version of this result. As a consequence, we obtain that for a continuous observable the phase transitions can occur at a countable dense set of temperature values. We go further and show that one can vary the cardinality of the set of ergodic equilibrium states as a function of the parameter to be any number, finite or infinite.
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