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We present a Monte Carlo study of the finite temperature properties of anextended Hubbard-Peierls model describing one dimensional $\pi$-conjugatedpolymers. The model incorporates electron-phonon and hyperfine interaction andit is solved at the mean field level for half filling. In particular we explorethe model as a function of the strength of electron-electron andelectron-phonon interactions. At low temperature the system presents adiamagnetic to antiferromagnetic transition as the electron-electroninteraction strength increases. At the same time by increasing theelectron-phonon coupling there is a transition from a homogeneous to a Peierlsdimerized geometry. As expected such a Peierls dimerized phase disappears atfinite temperature as a result of thermal vibrations. More intriguing is theinterplay between the electron-phonon and the electron-electron interactions atfinite temperature. In particular we demonstrate that for a certain region ofthe parameter space there is a spin-crossover, where the system transits from alow-spin to a high-spin state as the temperature increases. In close analogy tostandard spin-crossover in divalent magnetic molecules such a transition isentropy driven. Finally we discuss the role played by the hyperfine interactionover the phase diagram.

Monte-Carlo phase diagram of a Hubbard-Peierls model in the search for spin crossover transition in $\pi$-conjugated polymers