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We report on Hybrid-Monte-Carlo simulations at finite spin density of the$\pi$-band electrons in monolayer graphene with realistic inter-electroninteractions. Unlike simulations at finite charge-carrier density, these arenot affected by a fermion-sign problem. Our results are in qualitativeagreement with an interaction-induced warping of the Fermi contours, and areduction of the bandwidth as observed in angle resolved photoemissionspectroscopy experiments on charge-doped graphene systems. Furthermore, we findevidence that the neck-disrupting Lifshitz transition, which occurs when theFermi level traverses the van Hove singularity (VHS), becomes a true quantumphase transition due to interactions. This is in-line with an instability ofthe VHS towards the formation of electronic ordered phases, which has beenpredicted by a variety of different theoretical approaches.

A Hybrid-Monte-Carlo study of monolayer graphene with partially screened Coulomb interactions at finite spin density