Higher Spins and Matter Interacting in Dimension Three

The spectrum of Prokushkin--Vasiliev Theory is puzzling in light of the Gaberdiel--Gopakumar conjecture because it generically contains an additional sector besides higher-spin gauge and scalar fields. We find the unique truncation of the theory avoiding this problem to order 2 in perturbations around AdS$_3$. The second-order backreaction on the physical gauge sector induced by the scalars is computed explicitly. The cubic action for the physical fields is determined completely. We comment on a different higher-spin theory without such additional fields at $\lambda=1$.Comment: 55 pages + appendices, LaTex. Final version to appear in JHE

A Random Multifractal Tilling

We develop a multifractal random tilling that fills the square. The multifractal is formed by an arrangement of rectangular blocks of different sizes, areas and number of neighbors. The overall feature of the tilling is an heterogeneous and anisotropic random self-affine object. The multifractal is constructed by an algorithm that makes successive sections of the square. At each $n$-step there is a random choice of a parameter $\rho_i$ related to the section ratio. For the case of random choice between $\rho_1$ and $\rho_2$ we find analytically the full spectrum of fractal dimensions

Anisotropy and percolation threshold in a multifractal support

Recently a multifractal object, $Q_{mf}$, was proposed to study percolation properties in a multifractal support. The area and the number of neighbors of the blocks of $Q_{mf}$ show a non-trivial behavior. The value of the probability of occupation at the percolation threshold, $p_{c}$, is a function of $\rho$, a parameter of $Q_{mf}$ which is related to its anisotropy. We investigate the relation between $p_{c}$ and the average number of neighbors of the blocks as well as the anisotropy of $Q_{mf}$

Magnetic particles confined in a modulated channel: structural transitions tunable by tilting a magnetic field

The ground state of colloidal magnetic particles in a modulated channel are investigated as function of the tilt angle of an applied magnetic field. The particles are confined by a parabolic potential in the transversal direction while in the axial direction a periodic substrate potential is present. By using Monte Carlo (MC) simulations, we construct a phase diagram for the different crystal structures as a function of the magnetic field orientation, strength of the modulated potential and the commensurability factor of the system. Interestingly, we found first and second order phase transitions between different crystal structures, which can be manipulated by the orientation of the external magnetic field. A re-entrant behavior is found between two- and four-chain configurations, with continuous second order transitions. Novel configurations are found consisting of frozen in solitons. By changing the orientation and/or strength of the magnetic field and/or the strength and the spatial frequency of the periodic substrate potential, the system transits through different phases.Comment: Submitted to Phys. Rev. E (10 pages, 12 figures