▎ 摘　　要

We study the phase transition from disordered magnetic phase to fully polarized ferromagnetic phase of undoped gapped armchair graphene nanoribbon in the context of Hubbard model Hamiltonian. This phase transition has been investigated at zero temperature where magnetic phase ordering can take place for two dimensional systems. Ground state energy of electronic system has been found by using random phase approximation for both paramagnetic and fully polarized ferromagnetic phases. Energy gap between ferromagnetic and paramagnetic phases vanishes at critical electron density. Thus a spontaneous magnetic ordering develops for electron densities below critical value. The effects of ribbon width, gap parameter and electron-electron Hubbard interaction strength on critical electron density have been addressed. Our results show the increase of gap parameter raises the critical density and thus spontaneous phase transition occurs at higher density.