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We present the results of an analytical theory and simulations of the fieldinside a cavity created in a dipolar liquid placed in a uniform externalelectric field. The analytical theory shows that the limit of continuumelectrostatics is reached through a singularity in the microscopic responsefunction responsible for a non-decaying longitudinal polarization wave. Fieldsin microscopic cavities are much different from macroscopic predictions, andlow-polarity dielectrics are predicted to have a continuum limit distinct fromthe solution of Maxwell's equations. Computer Monte Carlo simulations neverreach the standard continuum limit and instead converge to the new continuumsolution with increasing cavity size.

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