Cavity field in liquid dielectrics

We present the results of an analytical model and simulations of the field inside a cavity in a uniformly polarized dipolar liquid. The analytical microscopic theory shows that Maxwell's equations of continuum electrostatics are realized through a singularity in the microscopic response function representing a non-decaying longitudinal polarization wave. The appearance of this solution depends on the order of continuum and thermodynamic limits taken in the microscopic equations. Fields in microscopic cavities are much different from macroscopic predictions approaching with increasing cavity size a new continuum expression derived from the microscopic equations. Numerical Monte Carlo simulations never reach the standard continuum limit and instead converge to a new continuum solution.