  The cactus approximation in the cluster variation method is applied to the
spin ice system with nearest neighbor ferromagnetic coupling. The temperature
dependences of the entropy and the specific heat show qualitatively good
agreement with those observed by Monte Carlo simulations and experiments, and
the Pauling value is reproduced for the residual entropy. The analytic
expression of the q-dependent magnetic susceptibility is obtained, from which
the absence of magnetic phase transition is confirmed. The neutron scattering
pattern is also evaluated and found to be consistent with that obtained from
Monte Carlo simulations.
