A heat capacity estimator for Fourier path integral simulations

Previous heat capacity estimators useful in path integral simulations have variances that grow with the number of path variables included. In the present work a new specific heat estimator for Fourier path integral Monte Carlo simulations is derived using methods similar to those used in developing virial energy estimators. The resulting heat capacity estimator has a variance that is roughly independent of the number of Fourier coefficients (k(max)) included, and the asymptotic convergence rate is shown to be proportional to 1/k(max)(2) when partial averaging is included. Quantum Monte Carlo simulations are presented to test the estimator using two one-dimensional models and for Lennard-Jones representations of Ne-13. For finite k(max), using numerical methods, the calculated heat capacity is found to diverge at low temperatures for the potential functions studied in this work. Extrapolation methods enable useful results to be determined over a wide temperature range. (C) 2000 American Institute of Physics. [S0021-9606(00)50809-5].