Path-integral Monte Carlo study of crystalline Lennard-Jones systems

The capability of the path-integral Monte Carlo (PIMC) method to describe thermodynamic and structural properties of solids at low temperatures is studied in detail, considering the noble-gas crystals as examples. In order to reduce the systematic limitations due to finite Trotter number and finite particle number we propose a combined Trotter and finite-size scaling. As a special application of the PIMC method we investigate ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ar}$ at constant volume and in the harmonic approximation. Furthermore, isotope effects in the lattice constant of ${}_{}{}^{20}{}_{}{}^{}\mathrm{Ne}$ and ${}_{}{}^{22}{}_{}{}^{}\mathrm{Ne}$ are computed at zero pressure. The obtained results are compared with classical Monte Carlo results and with experimental data.