A Monte Carlo method, combining a replica Monte Carlo simulation with a cumulant analysis of the generated replica energies, is employed in order to calculate efficiently and accurately the second-order, isothermal elastic constants of a defect-free, Lennard-Jones crystal. The advantages of this method are that it is easy to implement, that it does not require the calculation of stresses or their strain derivatives, and that only one constant-strain simulation is required. It is shown that other methods presently used to calculate elastic constants can be regarded, more generally, as alternative, cumulant expansions. This method is further extended to calculate higher-order elastic constants and, in particular, the dependence of the bulk modulus on strain.

• Received 12 December 1990

DOI:https://doi.org/10.1103/PhysRevB.43.13285