First-order chiral transition in the compact lattice theory of graphene and the case for improved actions

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A comparison of the compact and non-compact lattice versions of the low-energy theory of graphene is presented. The compact theory is found to exhibit a chiral phase transition which appears to be of first order, at a critical coupling of betac = 0.42 +/- 0.01. We confirm that the non-compact theory exhibits a second-order transition at betac = 0.072 +/- 0.003, and determine the effects of UV-divergent tadpole contributions in both cases. Upon tadpole improvement of the non-compact theory we find betacTI = 0.163 +/- 0.002, which strengthens the case for a semimetal-insulator transition in graphene at strong Coulomb coupling. Finally, we highlight the need for systematic studies using improved lattice actions.