  Recently, Mori [Phys. Rev. E 84, 031128 (2011)] has conjectured that the free
energy of Ising spin glass models with the Kac potential in the non-additive
limit, such as the power-law potential in the non-additive regime, is exactly
equal to that of the Sherrington-Kirkpatrick model in the thermodynamic limit.
In this study, we prove that his conjecture is true on the Nishimori line at
any temperature in any dimension. One of the key ingredients of the proof is
the use of the Gibbs-Bogoliubov inequality on the Nishimori line. We also
consider the case in which the probability distribution of the interaction is
symmetric, where his conjecture is true at any temperature in one dimension but
is an open problem in the low-temperature regime in two or more dimensions.
