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., relativistic like) dispersion relation for low energy quasiparticles. The general structure of the phase diagram of the theory with respect to the coupling constant, the chemical potential and temperature is derived in two cases, with and without an external magnetic field. The conductivity and resistivity as functions of temperature and magnetic field are studied in detail. An exact relation for the value of the "offset" magnetic field $B_c$, determining the threshold for the realization of the phase transition at zero temperature, is established. The theory is applied to the description of a recently observed phase transition induced by a magnetic field in highly oriented pyrolytic graphite.Comment: 22 pages, REVTeX, 16 figures. The version corresponding to that published in Phys.Rev.

The gap generation is studied in suspended clean graphene in the continuum model for quasiparticles with the Coulomb interaction. We solve the gap equation with the dynamical polarization function and show that, comparing to the case of the static polarization function, the critical coupling constant lowers to the value \alpha_c=0.92, which is close to that obtained in lattice Monte Carlo simulations. It is argued that additional short-range four-fermion interactions should be included in the continuum model to account for the lattice simulation results. We obtain the critical line in the plane of electromagnetic and four-fermion coupling constants and find a second order phase transition separating zero gap and gapped phases with critical exponents close to those found in lattice calculations.Comment: text slightly extended, one figure and references adde

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Reduced gauge theories are theories in which while gauge fields propagate in a bulk, fermion fields are localized on a brane. We study dynamical chiral symmetry breaking on a 2-brane and a 1-brane in reduced QED 3+1 , and on a 1-brane in reduced QED 2+1 . Since, unlike higher dimensional gauge theories, QED 3+1 and QED 2+1 are well defined, their reduced versions can serve as a laboratory for studying dynamics in a higher dimensional brane world. The analysis of the Schwinger-Dyson (SD) equations in these theories reveals rich and quite nontrivial dynamics in which the conformal symmetry and its breakdown play a crucial role. Explicit solutions of the SD equations in the near-critical regime are obtained and the character of the corresponding phase transition is described.11.10. Kk, 11.30.Qc,