Lattice Simulations near the Semimetal-Insulator Phase Transition of Graphene

We present results from Monte Carlo simulations of a three dimensional fermionic field theory which can be derived from a model of graphene in which electrons interact via a screened Coulomb potential. For our simulations we employ lattice gauge theory methods used in elementary particle physics. We show that the theory undergoes a second order phase transition and we provide estimates for the critical exponents. The estimated value of the physical critical coupling implies that graphene in vacuum is an insulator. We also present the first results for the quasiparticle dispersion relation.