Cavity Field in Molecular Liquids. When a Polar Liquid Becomes a Dielectric?

We present the results of an analytical theory and simulations of the field inside a cavity created in a dipolar liquid placed in a uniform external electric field. The analytical theory shows that the limit of continuum electrostatics is reached through a singularity in the microscopic response function responsible for a non-decaying longitudinal polarization wave. Fields in microscopic cavities are much different from macroscopic predictions, and low-polarity dielectrics are predicted to have a continuum limit distinct from the solution of Maxwell's equations. Computer Monte Carlo simulations never reach the standard continuum limit and instead converge to the new continuum solution with increasing cavity size.