Duality relations for elastic constants of the classical Gaussian core model

The many-body Gaussian core model involves a potential energy function that consists of a sum of repelling pair interactions, each of which is a simple Gaussian function of distance. This paper examines the linear elastic response of the model for its stable lattices at absolute zero temperature, in D=1, 2, and 3 dimensions. Owing to the fact that the Gaussian function is self-similar under Fourier transformation, exact relations exist connecting each elastic constant at number density rho to a partner at dual density rho(') in the reciprocal lattice, where rhorho(')=pi(-D). By using these identities, it has been possible to show that shear elastic constants in D=2 and 3 tend strongly to zero in the asymptotic high density limit.