Physics – Condensed Matter – Statistical Mechanics
Scientific paper
2003-07-31
J. Chem. Phys. 119, 12119 (2003)
Physics
Condensed Matter
Statistical Mechanics
11 pages, 4 figures
Scientific paper
10.1063/1.1625366
Previous heat capacity estimators used in path integral simulations either have large variances that grow to infinity with the number of path variables or require the evaluation of first and second order derivatives of the potential. In the present paper, we show that the evaluation of the total energy by the T-method estimator and of the heat capacity by the TT-method estimator can be implemented by a finite difference scheme in a stable fashion. As such, the variances of the resulting estimators are finite and the evaluation of the estimators requires the potential function only. By comparison with the task of computing the partition function, the evaluation of the estimators requires k + 1 times more calls to the potential, where k is the order of the difference scheme employed. Quantum Monte Carlo simulations for the Ne_13 cluster demonstrate that a second order central-difference scheme should suffice for most applications.
Doll J. D.
Freeman David L.
Predescu Cristian
Sabo Dubravko
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