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The Griffiths inequalities for Ising spin glasses are proved on the Nishimoriline with various bond randomness which includes Gaussian and $\pm J$ bondrandomness. The proof for Ising systems with Gaussian bond randomness hasalready been carried out by Morita et al, which uses not only the gauge theorybut also the properties of the Gaussian distribution, so that it cannot bedirectly applied to the systems with other bond randomness. The present proofessentially uses only the gauge theory, so that it does not depend on thedetail properties of the probability distribution of random interactions. Thus,the results obtained from the inequalities for Ising systems with Gaussian bondrandomness do also hold for those with various bond randomness, especially with$\pm J$ bond randomness.

Griffiths Inequalities for Ising Spin Glasses on the Nishimori Line