The Kubo linear response theory is applied to the quantum mechanical Ising model to obtain a general expression which is valid for all regular lattices for the perpendicular response function in terms of spin correlations. For the honeycomb and the square lattices, exact expressions are found for the frequency-dependent initial perpendicular susceptibility, [Formula: see text] valid for all temperatures. For the honeycomb lattice, the present result for zero frequency agrees with Fisher's static calculation, whereas there is disagreement in the case of the square lattice. The discrepancy is resolved by using an extended calculation which explicitly illustrates the difference between isothermal and adiabatic susceptibilities.