  In this study, we extend the lower bound on the average of the local energy
of the Ising model with quenched randomness [J. Phys. Soc. Jpn. 76, 074711
(2007)] obtained for a symmetric distribution to an asymmetric one. Compared
with the case of symmetric distribution, our bound has a non-trivial term. By
applying the acquired bound to a Gaussian distribution, we obtain the lower
bounds on the expectation of the square of the correlation function. Thus, we
demonstrate that in the Ising model in a Gaussian random field, the spin-glass
order parameter generally has a finite value at any temperature, regardless of
the forms of the other interactions.
