Exact solution on the magnetism and ferroelectricity in the Ising spin chain

► The realization of the decoupling between the lattice vibration and magnetic interactions. ► The exact results of the properties about the model. ► The maximum of the relative dielectric constant will be increased under a relative small magnetic field. ► Different next-nearest-neighbor exchange interactions of Mn ions will have different impact on the low-temperature susceptibility behaviors.