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The possible ferromagnetic ground state of a theoretical model proposed for quasi-one-dimensional organic polymer ferromagnets is investigated in detail. Within the self-consistent-field Hartree-Fock approximation, allowing for full. lattice relaxation, the system is studied self-consistently. We find a critical interaction, which is determined by the competition between the electron-electron interaction and the electron-phonon coupling. When electron-electron interaction is larger than the critical value, the ground state of the system is a stable ferromagnetic state. It is also found that in this stable ferromagnetic state the pi-electrons SDW will become very strong, and almost zero dimerization happens for the main chain.

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