Modulated phases and devil's staircases in a layered mean-field version of the ANNNI model

We investigate the phase diagram of a spin-$1/2$ Ising model on a cubic lattice, with competing interactions between nearest and next-nearest neighbors along an axial direction, and fully connected spins on the sites of each perpendicular layer. The problem is formulated in terms of a set of noninteracting Ising chains in a position-dependent field. At low temperatures, as in the standard mean-feild version of the Axial-Next-Nearest-Neighbor Ising (ANNNI) model, there are many distinct spatially commensurate phases that spring from a multiphase point of infinitely degenerate ground states. As temperature increases, we confirm the existence of a branching mechanism associated with the onset of higher-order commensurate phases. We check that the ferromagnetic phase undergoes a first-order transition to the modulated phases. Depending on a parameter of competition, the wave number of the striped patterns locks in rational values, giving rise to a devil's staircase. We numerically calculate the Hausdorff dimension $D_{0}$ associated with these fractal structures, and show that $D_{0}$ increases with temperature but seems to reach a limiting value smaller than $D_{0}=1$.Comment: 17 pages, 6 figure

Mimicking Nanoribbon Behavior Using a Graphene Layer on SiC

We propose a natural way to create quantum-confined regions in graphene in a system that allows large-scale device integration. We show, using first-principles calculations, that a single graphene layer on a trenched region of $[000\bar{1}]$ $SiC$ mimics i)the energy bands around the Fermi level and ii) the magnetic properties of free-standing graphene nanoribbons. Depending on the trench direction, either zigzag or armchair nanoribbons are mimicked. This behavior occurs because a single graphene layer over a $SiC$ surface loses the graphene-like properties, which are restored solely over the trenches, providing in this way a confined strip region.Comment: 4 pages, 4 figure

Tax evasion dynamics and Zaklan model on Opinion-dependent Network

Within the context of agent-based Monte-Carlo simulations, we study the well-known majority-vote model (MVM) with noise applied to tax evasion on Stauffer-Hohnisch-Pittnauer (SHP) networks. To control the fluctuations for tax evasion in the economics model proposed by Zaklan, MVM is applied in the neighborhood of the critical noise $q_{c}$ to evolve the Zaklan model. The Zaklan model had been studied recently using the equilibrium Ising model. Here we show that the Zaklan model is robust because this can be studied besides using equilibrium dynamics of Ising model also through the nonequilibrium MVM and on various topologies giving the same behavior regardless of dynamic or topology used here.Comment: 14 page, 4 figure

Constraints on Cold Dark Matter Accelerating Cosmologies and Cluster Formation

We discuss the properties of homogeneous and isotropic flat cosmologies in which the present accelerating stage is powered only by the gravitationally induced creation of cold dark matter (CCDM) particles ($\Omega_{m}=1$). For some matter creation rates proposed in the literature, we show that the main cosmological functions such as the scale factor of the universe, the Hubble expansion rate, the growth factor and the cluster formation rate are analytically defined. The best CCDM scenario has only one free parameter and our joint analysis involving BAO + CMB + SNe Ia data yields ${\tilde{\Omega}}_{m}= 0.28\pm 0.01$ ($1\sigma$) where $\tilde{{\Omega}}_{m}$ is the observed matter density parameter. In particular, this implies that the model has no dark energy but the part of the matter that is effectively clustering is in good agreement with the latest determinations from large scale structure. The growth of perturbation and the formation of galaxy clusters in such scenarios are also investigated. Despite the fact that both scenarios may share the same Hubble expansion, we find that matter creation cosmologies predict stronger small scale dynamics which implies a faster growth rate of perturbations with respect to the usual $\Lambda$CDM cosmology. Such results point to the possibility of a crucial observational test confronting CCDM with $\Lambda$CDM scenarios trough a more detailed analysis involving CMB, weak lensing, as well as the large scale structure.Comment: 12 pages, 3 figures, Accepted for publication by Physical Rev.