Path-Integral Monte Carlo Scheme for Rigid Tops: Application to the Quantum Rotator Phase Transition in Solid Methane

A new quantum propagator for asymmetric tops, exact for free tops, is applied to path-integral Monte Carlo simulations of quantum rotors. The algorithm does not suffer from the sign problem if the full density matrix is considered or if the identity representation for the density matrix is chosen. The method is applied to simulation of crystalline ${\mathrm{CH}}_4$, where the influence of quantum fluctuations in the lowering of the transition temperature from a plastic phase to an orientational ordered state is investigated. The possibility of an inverse hysteresis occurring at that transition is predicted and related to spin-statistical exchange effects.