Global equation of state and the phase transitions of the hard disc system

Abstract

The hard disc system plays a fundamental role in the study of two-dimensional matters. High-precision compressibility data and a complete picture of the phase transitions have been reported for all the phases and phase transition regions for the hard disc system with numerical simulation results. However, thorough descriptions of the system and phase transitions depend on analytical equations of state (EoS) over the entire density range, such that various thermodynamic properties can be calculated with the EoS. While majority of EoS’s published are for the stable fluid region only, few attempted the liquid-hexact transition region. All the EoS’s currently available are incapable of quantitative descriptions of the phase transitions. Here we construct a simple EoS to reproduce high-precision simulation data for all the stable liquid, liquid-hexatic transition region and hexatic phase. A global EoS is then obtained when the new EoS is smoothly united with a revisited EoS for the solid phase. Using this global equation, we are able to accurately identify all the phases and the phase transitions from the stable liquid to hexatic, then to solid phases.