Thirring模型中的相变
Phase transitions in Thirring's model
摘要：
在他关于负比热的开创性工作中，Walter Thirring引入了一个在微正则系综中可解的模型。在这里，我们给出了一个完整的描述，在微正则和正则系综的相图，突出系综不等价的主要特点。在这两个系综中，我们发现了一条一阶相变线，它在临界点结束。然而，无论是线还是点在两个系综的相图中的位置都不相同。我们还表明，微正则临界点和正则临界点可以分析地相互关联，分别使用熵和自由能的朗道展开，类似于[O.科恩，D. Mukamel，J. Stat.机械、P12017（2012）]。具有限制朗道展开的某些对称性的系统的例子已经在这篇参考文献中被考虑，而在Thirring的模型中没有这样的限制。这导致了一个相图，可以被看作是一个原型的粒子系统中发生的事情与运动自由度的主导作用是长程相互作用。
英文摘要：
In his pioneering work on negative specific heat, Walter Thirring in\-tro\-duced a model that is solvable in the microcanonical ensemble. Here, we give a complete description of the phase-diagram of this model in both the microcanonical and the canonical ensemble, highlighting the main features of ensemble inequivalence. In both ensembles, we find a line of first-order phase transitions which ends in a critical point. However, neither the line nor the point have the same location in the phase-diagram of the two ensembles. We also show that the microcanonical and canonical critical points can be analytically related to each other using a Landau expansion of entropy and free energy, respectively, in analogy with what has been done in [O. Cohen, D. Mukamel, J. Stat. Mech., P12017 (2012)]. Examples of systems with certain symmetries restricting the Landau expansion have been considered in this reference, while no such restrictions are present in Thirring's model. This leads to a phase diagram that can be seen as a prototype for what happens in systems of particles with kinematic degrees of freedom dominated by long-range interactions.
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