相关论文: Loop calculations for models of graphene
The three-dimensional Gross-Neveu model in $R^{1} \times S^{2}$ spacetime is considered at finite particles number density. We evaluate an effective potential of the composite scalar field $\sigma(x)$, which is expressed in terms of a…
We confirm earlier hints that the conventional phase diagram of the discrete chiral Gross-Neveu model in the large N limit is deficient at non-zero chemical potential. We present the corrected phase diagram constructed in mean field theory.…
The massive Gross-Neveu model is solved in the large N limit at finite temperature and chemical potential. The scalar potential is given in terms of Jacobi elliptic functions. It contains three parameters which are determined by…
We present high precision estimates of the exponents of a quantum phase transition in a planar antiferromagnet. This has been made possible by the recent development of cluster algorithms for quantum spin systems, the loop algorithms. Our…
We discuss the Monte Carlo method of simulating lattice field theories as a means of studying the low-energy effective theory of graphene. We also report on simulational results obtained using the Metropolis and Hybrid Monte Carlo methods…
We consider fermions on a honeycomb lattice supplemented by a spin invariant interaction that dynamically generates a quantum spin Hall insulator. This lattice model provides an instance of Gross-Neveu Heisenberg criticality, as realized…
We study scalar and chiral fermionic models in next-to-leading order with the help of the functional renormalisation group. Their critical behaviour is of special interest in condensed matter systems, in particular graphene. To derive the…
We study a Hermitian matrix model with the standard quartic potential amended by a $\mathrm{tr}(R\Phi^2)$ term for fixed external matrix $R$. This is motivated by a curvature term in the truncated Heisenberg algebra formulation of the…
Motivated by the success of the non-commutative scalar Grosse-Wulkenhaar model, a non-commutative U(1) gauge field theory including an oscillator-like term in the action has been put forward in arXiv:0705.4205. The aim of the current work…
We study the effect of anisotropy on phase transitions in graphene. We work with an low energy effective field theory which is strongly coupled, and solve a coupled set of Schwinger-Dyson equations. We show that the effect of anisotropy is…
We review the method of uniqueness which is a powerful technique for multi-loop calculations in higher dimensional theories with conformal symmetry. We use the method in momentum space and show that it allows a very transparent evaluation…
The low-energy theory of interacting electrons on graphene's two-dimensional honeycomb lattice is derived and discussed. In particular, the Hubbard model in the large-N limit is shown to have a semi-metal - antiferromagnetic insulator…
The phase diagram of the massive chiral Gross-Neveu model (the 1+1-dimensional Nambu-Jona-Lasinio model at large N) is investigated in the vicinity of the tricritical point. Using the derivative expansion, the grand canonical potential is…
Extending previous work on scalar field theories, we develop a quantum algorithm to compute relativistic scattering amplitudes in fermionic field theories, exemplified by the massive Gross-Neveu model, a theory in two spacetime dimensions…
An important yet largely unsolved problem in the statistical mechanics of disordered quantum systems is to understand how quenched disorder affects quantum phase transitions in systems of itinerant fermions. In the clean limit, continuous…
We study the instabilities to the conformal critical point of an exactly solvable family of Gross-Neveu models. Using conformal field theory techniques, we construct the zero-temperature phase diagram and identify the superconducting and…
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.…
We investigate nematic quantum phase transitions in two different Dirac fermion models. The models feature twofold and fourfold, respectively, lattice rotational symmetries that are spontaneously broken in the ordered phase. Using…
We study, for the first time, the phase structure of the Gross--Neveu model with a combination of a (constant) gravitational and a magnetic field. This has been made possible by our finding of an exact solution to the problem, namely the…
Using knowledge of the explicit $n$ dependence of the RG functions and expressions of critical exponents in the framework of large $N$ expansion in the Gross Neveu model we derive RG functions in 4- and 5-loop approximation.