An elastic Ising model for a one-dimensional diatomic spin chain is proposed to explain the ferroelectricity induced by the collinear magnetic order with a low-excited energy state. A statistical theory based on this model is developed to calculate the electrical and magnetic properties of Ca(3)CoMnO(6), a typical quasi-one-dimensional diatomic spin chain system. The calculated ferroelectric polarization and dielectric susceptibility show a good agreement with recently reported data on Ca(3)Co(2-x)Mn(x)O(6) (x approximate to 0.96) (Phys. Rev. Lett. 100 047601 (2008)), although the predicted magnetic susceptibility does not coincide well with experiment. We also address the rationality and deficiency of this model by including a first-order correction which improves the consistency between the model and experiment.
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