Magnetoinductance of Josephson junction array with frozen vortex diffusion

The dependence of sheet impedance of a Josephson junction array on an applied magnetic field is investigated in the regime when vortex diffusion between an array's plaquettes is effectively frozen due to a low enough temperature. The field-dependent correction to the sheet inductance is found to be proportional to $f\mathrm{ln}(1/f),$ where $f\ensuremath{\ll}1$ is the magnitude of the field expressed in terms of flux quanta per plaquette.