Long-time behavior of MHD shell models

The long time behavior of velocity-magnetic field alignment is numerically investigated in the framework of MHD shell model. In the stationary forced case, the correlation parameter C displays a nontrivial behavior with long periods of high variability which alternates with periods of almost constant C. The temporal statistics of correlation is shown to be non Poissonian, and the pdf of constant sign periods displays clear power law tails. The possible relevance of the model for geomagnetic dynamo problem is discussed.Comment: 6 pages with 5 figures. In press on Europhysics Letter

Spin polarization and g-factor enhancement in graphene nanoribbons in magnetic field

We provide a systematic quantitative description of spin polarization in armchair and zigzag graphene nanoribbons in a perpendicular magnetic field. We first address spinless electrons within the Hartree approximation studying the evolution of the magnetoband structure and formation of the compressible strips. We discuss the potential profile and the density distribution near the edges and the difference and similarities between armchair and zigzag edges. Accounting for the Zeeman interaction and describing the spin effects via the Hubbard term we study the spin-resolved subband structure and relate the spin polarization of the system at hand to the formation of the compressible strips for the case of spinless electrons. At high magnetic field the calculated effective g-factor varies around a value of ~2.25 for armchair nanoribbons and ~3 for zigzag nanoribbons. An important finding is that in zigzag nanoribbons the zero-energy mode remains pinned to the Fermi-energy and becomes fully spin-polarized for all magnetic fields, which, in turn, leads to a strong spin polarization of the electron density near the zigzag edge.Comment: 9 pages, 4 figure

Universal finite size corrections and the central charge in non solvable Ising models

We investigate a non solvable two-dimensional ferromagnetic Ising model with nearest neighbor plus weak finite range interactions of strength \lambda. We rigorously establish one of the predictions of Conformal Field Theory (CFT), namely the fact that at the critical temperature the finite size corrections to the free energy are universal, in the sense that they are exactly independent of the interaction. The corresponding central charge, defined in terms of the coefficient of the first subleading term to the free energy, as proposed by Affleck and Blote-Cardy-Nightingale, is constant and equal to 1/2 for all 0<\lambda<\lambda_0 and \lambda_0 a small but finite convergence radius. This is one of the very few cases where the predictions of CFT can be rigorously verified starting from a microscopic non solvable statistical model. The proof uses a combination of rigorous renormalization group methods with a novel partition function inequality, valid for ferromagnetic interactions.Comment: 43 pages, 1 figur

Striped periodic minimizers of a two-dimensional model for martensitic phase transitions

In this paper we consider a simplified two-dimensional scalar model for the formation of mesoscopic domain patterns in martensitic shape-memory alloys at the interface between a region occupied by the parent (austenite) phase and a region occupied by the product (martensite) phase, which can occur in two variants (twins). The model, first proposed by Kohn and Mueller, is defined by the following functional: $${\cal E}(u)=\beta||u(0,\cdot)||^2_{H^{1/2}([0,h])}+ \int_{0}^{L} dx \int_0^h dy \big(|u_x|^2 + \epsilon |u_{yy}| \big)$$ where $u:[0,L]\times[0,h]\to R$ is periodic in $y$ and $u_y=\pm 1$ almost everywhere. Conti proved that if $\beta\gtrsim\epsilon L/h^2$ then the minimal specific energy scales like $\sim \min\{(\epsilon\beta/L)^{1/2}, (\epsilon/L)^{2/3}\}$, as $(\epsilon/L)\to 0$. In the regime $(\epsilon\beta/L)^{1/2}\ll (\epsilon/L)^{2/3}$, we improve Conti's results, by computing exactly the minimal energy and by proving that minimizers are periodic one-dimensional sawtooth functions.Comment: 29 pages, 3 figure

Froth-like minimizers of a non local free energy functional with competing interactions

We investigate the ground and low energy states of a one dimensional non local free energy functional describing at a mean field level a spin system with both ferromagnetic and antiferromagnetic interactions. In particular, the antiferromagnetic interaction is assumed to have a range much larger than the ferromagnetic one. The competition between these two effects is expected to lead to the spontaneous emergence of a regular alternation of long intervals on which the spin profile is magnetized either up or down, with an oscillation scale intermediate between the range of the ferromagnetic and that of the antiferromagnetic interaction. In this sense, the optimal or quasi-optimal profiles are "froth-like": if seen on the scale of the antiferromagnetic potential they look neutral, but if seen at the microscope they actually consist of big bubbles of two different phases alternating among each other. In this paper we prove the validity of this picture, we compute the oscillation scale of the quasi-optimal profiles and we quantify their distance in norm from a reference periodic profile. The proof consists of two main steps: we first coarse grain the system on a scale intermediate between the range of the ferromagnetic potential and the expected optimal oscillation scale; in this way we reduce the original functional to an effective "sharp interface" one. Next, we study the latter by reflection positivity methods, which require as a key ingredient the exact locality of the short range term. Our proof has the conceptual interest of combining coarse graining with reflection positivity methods, an idea that is presumably useful in much more general contexts than the one studied here.Comment: 38 pages, 2 figure

Effect of nonhomogenous dielectric background on the plasmon modes in graphene double-layer structures at finite temperatures

We have calculated the plasmon modes in graphene double layer structures at finite temperatures, taking into account the inhomogeneity of the dielectric background of the system. The effective dielectric function is obtained from the solution of the Poisson equation of three-layer dielectric medium with the graphene sheets located at the interfaces, separating the different materials. Due to the momentum dispersion of the effective dielectric function, the intra- and inter-layer bare Coulomb interactions in the graphene double layer system acquires an additional momentum dependence--an effect that is of the order of the inter-layer interaction itself. We show that the energies of the in-phase and out-of-phase plasmon modes are determined largely by different values of the spatially dependent effective dielectric function. The effect of the dielectric inhomogeneity increases with temperature and even at high temperatures the energy shift induced by the dielectric inhomogeneity and temperature itself remains larger than the broadening of the plasmon energy dispersions due to the Landau damping. The obtained new features of the plasmon dispersions can be observed in frictional drag measurements and in inelastic light scattering and electron energy-loss spectroscopies.Comment: 5 pages, 3 figure