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as shown in Fig.3(b), and also because the nodes of the f -wave gap do not intersect the Fermi surface. 

Nonetheless, as can be seen from Fig.2, the tempera- ture at which the f -wave eigenvalue reaches unity, if any, seems to be very low. We have also tried a model that considers the nearest neighbor off-site interaction V in addition to U . In this case, strong charge fluctuations arise, which makes the triplet vs. singlet competition more subtle, but in any case, the eigenvalue of the Eliash- berg equation remained small even when the magnitude of V is close to the point where the charge susceptibility diverges. Considering the experimental fact that the T$_{c}$ is relatively high in the doped β -MNCl, and also that 

the pairing occurs in the spin singlet channel $^{13}$, we be- lieve that the single band model does not suffice as an effective model for β -MNCl. 

## IV. TWO BAND MODEL : CALCULATION RESULTS 

## A. Superconducting transition temperature 

We now move on to the two band model. In this model, we find that spin singlet pairing strongly dominates over triplet pairing. In Fig.4, we plot T$_{c}$ of the singlet pairing superconductivity as a function of the band filling. It can be seen that T$_{c}$ ∼ 30K is obtained, which can be consid- ered as relatively high noting that T$_{c}$ ∼ 100K (assuming t ∼ 0 . 4eV appropriate for the cuprates) is obtained by the same method for the Hubbard model on the square lattice. 23 The difference between the single and two band models is dramatic in that not only the T$_{c}$ but even the leading pairing symmetry is different. This is in con- trast to the case of the cuprates, where the single band Hubbard and three band d - p models is expected to give roughly the same conclusions. 

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The high T$_{c}$ obtained in this model can be understood as a combination of several features of this model. Let us start with a canonical HC lattice, where t ′ = 0 and Δ = 0. We show in Fig.5(a) the FLEX result of the maximum value of the spin susceptibility as a function of temperature for the band filling of n = 1 . 08. The spin susceptibility is nearly independent of T , 15,27 which is in sharp contrast with the Hubbard model on the square lat- tice. For example, for the square lattice with n = 0 . 7, we have a strong enhancement of the spin susceptibility upon lowering the temperature. With further hole doping to n = 0 . 65, the spin susceptibility is suppressed, but even 

