Center for Design, Manufacturing and Materials, Skolkovo Institute of Science and Technology, Bolshoy Boulevard 30, Moscow 121205, Russia.
Phys Rev E. 2019 Nov;100(5-1):052118. doi: 10.1103/PhysRevE.100.052118.
Lee-Yang and Fisher zeros are crucial for the study of phase transitions in the grand canonical and the canonical ensembles, respectively. However, these powerful methods do not cover the isothermal-isobaric ensemble (NPT ensemble), which reflects the conditions of many experiments. In this work we present a theory of the phase transitions in terms of the zeros of the NPT-ensemble partition functions in the complex plane. The proposed theory provides an approach to calculate all the partition function zeros in the NPT ensemble, which form certain curves in the thermodynamic limit. To verify the theory we consider Tonks gas and van der Waals fluid in the NPT ensemble. In the case of Tonks gas, similarly to the Lee-Yang circle theorem, we obtain an exact equation for the zero limit curve. We also derive an approximated limit curve equation for van der Waals fluid in terms of the Szegö curve. This curve fits numerically calculated zeros and correctly describes how the phenomenon of phase transition depends on the temperature.
李-杨零点和费舍尔零点分别对巨正则系综和正则系综中的相变研究至关重要。然而，这些强大的方法并不涵盖等温和等压系综（NPT 系综），这反映了许多实验的条件。在这项工作中，我们提出了一种基于复平面上 NPT 系综配分函数零点的相变理论。所提出的理论提供了一种计算 NPT 系综中所有配分函数零点的方法，这些零点在热力学极限下形成某些曲线。为了验证该理论，我们考虑了 NPT 系综中的 Tonks 气体和范德华流体。在 Tonks 气体的情况下，类似于李-杨圆定理，我们得到了零点极限曲线的精确方程。我们还基于 Szegő 曲线推导出了范德华流体的近似极限曲线方程。该曲线拟合了数值计算的零点，并正确描述了相变现象如何随温度变化。
