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We study the electronic states of quasi-one-dimensional organic conductors using the single band Hubbard model at half-filling. We treat the effects of the on-site Coulomb interaction by the fluctuation-exchange (FLEX) method, and calculate the phase diagram and physical properties. The calculated pressure dependence of the Neel temperature coincides well with the experimental one. We also show that a pseudogap is formed in the density of states near the chemical potential and that d-wave superconductivity appears next to the antiferromagnetic state. Moreover the NMR relaxation rate increases on cooling in the low-temperature region.

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