Mean-field quantum phase transition in graphene and in general gapless systems

We study the quantum-critical properties of antiferromagnetism in graphene at T = 0 within mean-field (MF) theory. The resulting exponents differ from the conventional MF exponents, describing finite-temperature transitions. Motivated by this, we have developed the MF theory of general gapless phases with density of states p(epsilon) similar to vertical bar epsilon vertical bar(r), r > -1, with the interaction as control parameter. For r > 2, the conventional MF exponents a la Landau are recovered, while for -1 < r < 2, the exponents vary significantly with r. The critical interaction is finite for r > 0, therefore no weak-coupling solution exists in this range. This generalizes the results on quantum criticality of the gapless Kondo systems to bulk correlated phases.