  The Griffiths inequalities for Ising spin-glass models with Gaussian
randomness of non-vanishing mean are proved using properties of the Gaussian
distribution and gauge symmetry of the system. These inequalities imply that
correlation functions are non-negative and monotonic along the Nishimori line
in the phase diagram. From this result, the existence of thermodynamic limit
for correlation functions and pressure is proved under free and fixed boundary
conditions. Relations between the location of multicritical points are also
derived for different lattices.
