Dynamic Susceptibility of a Spin Ice near the Critical Point

We consider spin ice magnets (primarily, Dy2Ti2O7 in the vicinity of their critical point on the (H, T) plane. We find that the longitudinal susceptibility diverges at the critical point, leading to the behavior qualitatively similar to the one which would result from non-zero conductance of magnetic charges. We show that dynamics of critical fluctuations belongs to the universality class of easy-axis ferroelectric and calculate logarithmic corrections (within two-loop approximation) to the mean-field critical behavior.