Elastic constants from microscopic strain fluctuations

Fluctuations of the instantaneous local Lagrangian strain epsilon(ij)(r,t), measured with respect to a static "reference" lattice, are used to obtain accurate estimates of the elastic constants of model solids from atomistic computer simulations. The measured strains are systematically coarse-graine d by averaging them within subsystems (of size L-b) Of a system (of total s ize L) in the canonical ensemble. Using a simple finite size scaling theory we predict the behavior of the fluctuations <epsilon(ij)epsilon(kl)> as a function of L-b/L and extract elastic constants of the system in the thermo dynamic limit at nonzero temperature. Our method is simple to implement, ef ficient, and general enough to be able to handle a wide class of model syst ems, including those with singular potentials without any essential modific ation. We illustrate the technique by computing isothermal elastic constant s of "hard" and "soft" disk triangular solids in two dimensions from Monte Carlo and molecular dynamics simulations. We compare our results with those from earlier simulations and theory.