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We report a thorough study of the reducibility of edge correlation effects ingraphene to much-simplified effective models for the edge states. The latterhave been used before in specially tailored geometries. By a systematicinvestigation of corrections due to the bulk states in second orderperturbation theory, we show that the reduction to pure edge state models iswell-justified in general geometries. The framework of reduced models discussedhere enables the study of non-mean-field correlation physics for system sizesfar beyond the reach of conventional methods, such as, e.g., quantumMonte-Carlo.

Effective spin theories for edge magnetism in graphene zigzag ribbons