The zeros of the partition function in NPT-ensemble.

The knowledge about the zeros of the partition function is crucial for study of phase transitions. This topic has long history and powerful approaches were developed for canonical and grand canonical ensembles. The current work considers isothermal-isobaric ensemble (NPT-ensemble) which is one of the most relevant for the modeling of the experimental conditions, especially in the case of phase transitions. We have obtained a novel expression for real fluid partition function in NPT-ensemble represented in terms of cluster integrals. Our approach allows to avoid density limitations and to obtain the zeros of the partition function in NPT-ensemble. This method has been tested on well studied systems such as Tonks gas and van der Waals fluid. In the first case, our theoretical results for the distribution of the zeros in the thermodynamic limit have excellent agreement with direct calculations. In the second case we have calculated the zeros distribution and proposed the equation of the limit curve for the zeros in NPT-ensemble. This curve fits calculated zeros well and correctly describes the phenomenon of phase transition.