# Renormalization group flow of quartic perturbations in graphene: Strong coupling and large- N limits

@article{Drut2008RenormalizationGF,
title={Renormalization group flow of quartic perturbations in graphene: Strong coupling and large- N limits},
author={Joaqu{\'i}n E. Drut and Dam Thanh Son},
journal={Physical Review B},
year={2008},
volume={77},
pages={075115}
}
• Published 5 October 2007
• Physics
• Physical Review B
We explore the renormalization group flow of quartic perturbations in the low-enegy theory of graphene, in the strong Coulomb coupling and large-$N$ limits, where $N$ is the number of fermion flavors. We compute the anomalous dimensions of the quartic couplings $u$ up to leading order in $1∕N$ and find both relevant and irrelevant directions in the space of quartic couplings. We discuss possible phase diagrams and relevance for the physics of graphene.
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## References

SHOWING 1-10 OF 18 REFERENCES
Non-Fermi liquid behavior of electrons in the half-filled honeycomb lattice (A renormalization group approach)
• Physics
• 1994
A system of electrons in the two-dimensional honeycomb lattice with Coulomb interactions is described by a renormalizable quantum field theory similar but not equal to QED3. Renormalization group
Interactions and phase transitions on graphene's honeycomb lattice.
• I. Herbut
• Physics, Medicine
Physical review letters
• 2006
The Hubbard model in the large-N limit is shown to have a semimetal-antiferromagnetic insulator quantum critical point in the universality class of the Gross-Neveu model, and its consequences for various physical quantities are examined.
Quantum critical point in graphene approached in the limit of infinitely strong Coulomb interaction
Motivated by the physics of graphene, we consider a model of $N$ species of $2+1$ dimensional four-component massless Dirac fermions interacting through a three dimensional instantaneous Coulomb
Critical flavor number in the three dimensional Thirring model
• Physics
• 2007
We present results of a Monte Carlo simulation of the three dimensional Thirring model with the number of fermion flavors N{sub f} varied between 2 and 18. By identifying the lattice coupling at
Coulomb Interactions and Ferromagnetism in Pure and Doped Graphene
• Materials Science, Physics
• 2005
We study the presence of ferromagnetism in the phase diagram of the two-dimensional honeycomb lattice close to half-filling (graphene) as a function of the strength of the Coulomb interaction and
Excitonic instability in layered degenerate semimetals
• Physics
• 2004
Abstract We study excitonic pairing in quasi-two-dimensional degenerate semimetals such as graphite, where the electron density of states nearly vanishes at the Fermi level and, therefore, the
Spontaneous symmetry breakings in graphene subjected to in-plane magnetic field
• Physics
• 2007
Application of the magnetic field parallel to the plane of the graphene sheet leads to the formation of electron- and holelike Fermi surfaces. Such situation is shown to be unstable with respect to
Dynamical symmetry breaking in asymptotically free field theories
• Physics
• 1974
Two-dimensional massless fermion field theories with quartic interactions are analyzed. These models are asymptotically free. The models are expanded in powers of $\frac{1}{N,}$ where $N$ is the
Magnetic field driven metal insulator phase transition in planar systems
• Materials Science, Physics
• 2002
A theory of the magnetic field driven (semi)metal-insulator phase transition is developed for planar systems with a low density of carriers and a linear (i.e., relativisticlike) dispersion relation