Effective spin theories for edge magnetism in graphene zigzag ribbons

We report a thorough study of the reducibility of edge correlation effects in graphene to much simplified effective models for the edge states. The latter have been used before in specially tailored geometries. By a systematic investigation of corrections due to the bulk states in second-order perturbation theory, we show that the reduction to pure edge state models is well justified in general geometries. The framework of reduced models discussed here enables the study of non-mean-field correlation physics for system sizes far beyond the reach of conventional methods, such as, e.g., quantum Monte Carlo.