Upper and lower bounds to a correlation function for an Ising model with random interactions

We consider the general Ising model with random interactions Jp. We assume that the probability densities of the random interactions are statistically independent and that the averages of the absolute values of the random interactions, |Jp|, are finite. We then show that a correlation function for the regular Ising model with interactions |Jp| and the same quantity with opposite sign are an upper and a lower bound to the corresponding averaged correlation function of the random Ising model under consideration.