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We prove that the distribution functions of magnetization and spin glassorder parameter coincide on the Nishimori line in the phase diagram of the $\pmJ$ Ising model in any dimension. This implies absence of replica symmetrybreaking because the distribution function of magnetization consists only oftwo delta functions, suggesting the same simple structure for the distributionof spin glass order parameter. It then follows that the mixed (glassy) phase,where the ferromagnetic order coexists with complex phase space, should lie, ifany, below the Nishimori line. We also argue that the AT line to mark the onsetof RSB with a continous distribution of the spin glass order parameter, if anyagain, would start with an infinite slope from the multicritical point whereparamagnetic, ferromagnetic and spin glass phases merge.Comment: 6 pages, 3 figures, uses aipproc.st

Absence of replica symmetry breaking in a region of the phase diagram of the Ising spin glass