Numerical evidence of conformal phase transition in graphene with long-range interactions

Understand

Using state of the art Hybrid-Monte-Carlo (HMC) simulations we carry out an unbiased study of the competition between spin-density wave (SDW) and charge-density wave (CDW) order in suspended graphene.

• We determine that the realistic inter-electron potential of graphene must be scaled up by a factor of roughly 1.6 to induce a semimetal-SDW phase transition and find no evidence for CDW order.
• A study of critical properties suggests that the universality class of the three-dimensional chiral Heisenberg Gross-Neveu model with two fermion flavors, predicted by renormalization group studies and strong-coupling expansion, is unlikely to apply to this transition.
• We propose that our results instead favor an interpretation in terms of a conformal phase transition.