Magnetization plateaus in the Ising limit of the multiple-spin exchange model on plaquette chain

We consider the Ising spin system, which stems out from the corresponding Multiple-spin exchange (MSE) Hamiltonian, on the special one--dimensional lattice, diamond-plaquette chain. Using the technique e of transfer-matrix we obtain the exact expression for system free energy with the aid of which we obtain the magnetization function. Analyzing magnetization curves for varies values of temperature and couplin constants we found the magnetization plateaux at 1/3 and 2/3 of the full moment. The corresponding microscopic spin configurations are unknown by virtue of high frustration.