Path integral Monte Carlo simulations for pair correlation function for liquid 4He systems

Abstract

Path integral Monte Carlo (PIMC) simulation is a powerful tool in studying the interacting quantum systems at finite temperatures. In this article, we use PIMC to study the pair correlation function g(r) of the system consisting of 124 4He atoms in different conditions. At saturated-vapor-pressure (SVP), we calculated the pair correlation function g(r) at four different temperatures respectively, that is, T=138 K, 167 K, 250 K and 424 K. We also determined the changes in g(r) when either temperature or density is changed while the other remaines fixed, and found that for different densities and the same temperature, the change in g(r) is remarkable, while for different temperatures but same density, the change is not obvious. We used the microcosmic point of view for g(r) to explain the above phenomenon. Although finite size effects exist in the PIMC method, when comparing the pair correlation function belonging to systems consisted of 128 and 256 4He atoms respectively, differences between them are small. And we can conclude that as the increasing of the simulated system size, differences between simulated system and the real one becomes smaller and smaller. So in this particle, the properties educed from the simulated system consisted of 256 4He atoms can represent those of the real liquid system.