Universality in fermionic field theories at finite temperature

We discuss the critical properties of the three-dimensional NJL model at nonzero temperature. We show that the Z(2)-symmetric model undergoes a second order phase transition with 2d Ising exponents and its critical region is suppressed by a factor 1/N^{-0.5}. We also provide numerical evidence that the U(1)-symmetric model undergoes a BKT transition in accordance with the dimensional reduction scenario.Comment: 5 pages, Contribution to Conference on Strong and Electroweak Matter (SEWM2002), Heidelberg, Germany, 2-5 Oct. 200

Quantum Critical Behaviour in a Graphene-like Model

We present the first results of numerical simulations of a 2+1 dimensional fermion field theory based on a recent proposal for a model of graphene, consisting of N_f four-component Dirac fermions moving in the plane and interacting via an instantaneous Coulomb interaction. In the strong-coupling limit we identify a critical number of flavors N_fc=4.8(2) separating an insulating from a conducting phase. This transition corresponds to the location of a quantum critical point, and we use a fit to the equation of state for the chiral order parameter to estimate the critical exponents. Next we simulate N_f=2 corresponding to real graphene, and approximately locate a transition from strong to weak coupling behaviour. Strong correlations are evident in the weak-coupling regime.Comment: 14 pages, 6 figure

Monte Carlo Simulation of the Semimetal-Insulator Phase Transition in Monolayer Graphene

A 2+1 dimensional fermion field theory is proposed as a model for the low-energy electronic excitations in monolayer graphene. The model consists of N=2 four-component Dirac fermions moving in the plane and interacting via a contact interaction between charge densities. For strong couplings there is a continuous transition to a Mott insulting phase. We present results of an extensive numerical study of the model's critical region, including the order parameter, its associated susceptibility, and for the first time the quasiparticle propagator. The data enables an extraction of the critical exponents at the transition, including the dynamical critical exponent, which are hypothesised to be universal features of a quantum critical point. The relation of our model with others in the literature is discussed, along with the implications for physical graphene following from our value of the critical coupling.Comment: 19 page

Three dimensional four-fermion models - A Monte Carlo study

We present results from numerical simulations of three different 3d four-fermion models that exhibit Z_2, U(1), and SU(2) x SU(2) chiral symmetries, respectively. We performed the simulations by using the hybrid Monte Carlo algorithm. We employed finite size scaling methods on lattices ranging from 8^3 to 40^3 to study the properties of the second order chiral phase transition in each model. The corresponding critical coupling defines an ultraviolet fixed point of the renormalization group. In our high precision simulations, we detected next-to-leading order corrections for various critical exponents and we found them to be in good agreement with existing analytical large-N_f calculations.Comment: 15 pages, 7 figures, and 2 table

Quantum Phase Transition in a Graphene Model

We present results for the equation of state of a graphene-like model in an effort to understand the properties of its quantum phase transition. The N_f fermion species interact through a three dimensional instantaneous Coulomb potential. Since there are no reliable analytical tools that work for all values of N_f and the coupling constant g, we rely on Monte Carlo simulations to calculate the critical properties of the model near the phase transition. We consider the four-component formulation for the fermion fields, which arises naturally as the continuum limit of the staggered fermion construction in (2+1) dimensions. In the limit of infinitely strong Coulomb interaction, the system undergoes a quantum phase transition at a critical number of fermion species N_fc ~ 4.7. We also calculate the values of the critical exponents at the quantum phase transition.Comment: 4 pages, 3 figures, presented at the 25th international conference on Low Temperature Physics, 6-13 August 2008, Amsterda

Mesons at finite baryon density in (2+1)d

We discuss the critical properies of the three-dimensional Gross-Neveu model at nonzero temperature and nonzero chemical potential. We also present numerical and analytical results for the in-medium interaction due to scalar meson exchange. Further, we discuss in-medium modifications of mesonic dispersion relations and wavefunctions.Comment: 9 pages, 5 figures, Contribution to Workshop on Finite Density QCD at Nara, Japan, July 10-12 200