Temperature-and-density-scaling Monte Carlo: isothermal-isobaric thermodynamics of Lennard-Jonesium

In the "thermodynamic limit" thermodynamic quantities have the same values regardless of the ensemble in which they may be generated, but this is by no means the case for the small systems to which simulations are restricted. A preceding paper ["Temperature-and-density-scaling Monte Carlo: methodology and the canonical thermodynamics of Lennard-Jonesium" Molecular Simulation 2005] discussed temperature-and-density-scaling Monte Carlo, and used the results of one such run to generate accurate thermodynamic data for Lennard-Jones fluids in the canonical ensemble, continuously throughout a substantial region of temperature and density. This paper demonstrates how the same data can instead be used to generate the accurate thermodynamics of the system within the isothermal-isobaric ensemble, now continuously throughout a substantial region of temperature and pressure. This evidently constitutes an alternative method of generating precise isothermal-isobaric thermodynamics, one which may often be particularly efficient. Results in the canonical and isothermal-isobaric ensembles are compared in some detail; the discrepancy of behaviour in the coexistence and critical regions is of course striking; nevertheless the two ensembles bracket the limiting coexistence behaviour rather closely. Some preliminary analysis of the critical behaviour is carried out, but a fully-detailed finite-size scaling analysis is deferred.