从配分函数渐近表示的极点出发的一阶相变
First-order phase transitions from poles in asymptotic representations of partition functions
摘要：
虽然有限尺寸系统的配分函数总是解析的，因此没有极点，但它们在许多情况下可以表示为包含极点项的级数。在这里，我们表明，这样的极点可以与线性分支的熵，表示在热力学极限为每个粒子的能量的函数。我们还表明，这些极点可以用来确定熵是否是非凹的或具有线性部分，这是不能做的事情与来自配分函数的热力学自由能的唯一知识。我们讨论具有一阶相变的平衡系统的应用。
英文摘要：
Although partition functions of finite-size systems are always analytic, and hence have no poles, they can be expressed in many cases as series containing terms with poles. Here we show that such poles can be related to linear branches of the entropy, expressed in the thermodynamic limit as a function of the energy per particle. We also show that these poles can be used to determine whether the entropy is nonconcave or has linear parts, which is something that cannot be done with the sole knowledge of the thermodynamic free energy derived from the partition function. We discuss applications for equilibrium systems having first-order phase transitions.
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