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Magnetic and thermodynamic properties of the zigzag graphene nanoribbon described by Ising model have been studied within Monte Carlo simulation. The system exhibited interesting and rich magnetization plateaus behaviors at low temperature, which is sensitive to the exchange coupling and the anisotropy. In certain parameters, the depressed saturation magnetization, spin-flip or spin-flop has been found on the magnetization curves. The peaks on the susceptibility and specific heat curves originate from competition among the magnetic field, the exchange couplings and anisotropies. The spin configurations of the zigzag graphene nanoribbon can be modulated by the anisotropies. Our results can provide an opportunity for the design of a new type random access memory by using zigzag graphene nanoribbon. • Ising model of zigzag graphene nanoribbon is suggested. • Magnetic properties of the system have been studied. • spin-flip or spin-flop has been found on the magnetization curves. [ABSTRACT FROM AUTHOR]