Higher Order and boundary Scaling Fields in the Abelian Sandpile Model

The Abelian Sandpile Model (ASM) is a paradigm of self-organized criticality (SOC) which is related to $c=-2$ conformal field theory. The conformal fields corresponding to some height clusters have been suggested before. Here we derive the first corrections to such fields, in a field theoretical approach, when the lattice parameter is non-vanishing and consider them in the presence of a boundary.Comment: 7 pages, no figure

Boundary conditions and defect lines in the Abelian sandpile model

We add a defect line of dissipation, or crack, to the Abelian sandpile model. We find that the defect line renormalizes to separate the two-dimensional plane into two half planes with open boundary conditions. We also show that varying the amount of dissipation at a boundary of the Abelian sandpile model does not affect the universality class of the boundary condition. We demonstrate that a universal coefficient associated with height probabilities near the defect can be used to classify boundary conditions.Comment: 8 pages, 1 figure; suggestions from referees incorporated; to be published in Phys. Rev.

Turbulence generation in homogeneous particle-laden flows

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/76730/1/AIAA-1998-240-706.pd

Selective interlayer ferromagnetic coupling between the Cu spins in YBa2_2 Cu3_3 O7−x_{7-x} grown on top of La0.7_{0.7} Ca0.3_{0.3} MnO3_3

Studies to date on ferromagnet/d-wave superconductor heterostructures focus mainly on the effects at or near the interfaces while the response of bulk properties to heterostructuring is overlooked. Here we use resonant soft x-ray scattering spectroscopy to reveal a novel c-axis ferromagnetic coupling between the in-plane Cu spins in YBa$_2$ Cu$_3$ O$_{7-x}$ (YBCO) superconductor when it is grown on top of ferromagnetic La$_{0.7}$ Ca$_{0.3}$ MnO$_3$ (LCMO) manganite layer. This coupling, present in both normal and superconducting states of YBCO, is sensitive to the interfacial termination such that it is only observed in bilayers with MnO_2but not with La$_{0.7}$ Ca$_{0.3}$ interfacial termination. Such contrasting behaviors, we propose, are due to distinct energetic of CuO chain and CuO$_2$ plane at the La$_{0.7}$ Ca$_{0.3}$ and MnO$_2$ terminated interfaces respectively, therefore influencing the transfer of spin-polarized electrons from manganite to cuprate differently. Our findings suggest that the superconducting/ferromagnetic bilayers with proper interfacial engineering can be good candidates for searching the theorized Fulde-Ferrel-Larkin-Ovchinnikov (FFLO) state in cuprates and studying the competing quantum orders in highly correlated electron systems.Comment: Please note the change of the title. Text might be slightly different from the published versio

Vacancy localization in the square dimer model

We study the classical dimer model on a square lattice with a single vacancy by developing a graph-theoretic classification of the set of all configurations which extends the spanning tree formulation of close-packed dimers. With this formalism, we can address the question of the possible motion of the vacancy induced by dimer slidings. We find a probability 57/4-10Sqrt[2] for the vacancy to be strictly jammed in an infinite system. More generally, the size distribution of the domain accessible to the vacancy is characterized by a power law decay with exponent 9/8. On a finite system, the probability that a vacancy in the bulk can reach the boundary falls off as a power law of the system size with exponent 1/4. The resultant weak localization of vacancies still allows for unbounded diffusion, characterized by a diffusion exponent that we relate to that of diffusion on spanning trees. We also implement numerical simulations of the model with both free and periodic boundary conditions.Comment: 35 pages, 24 figures. Improved version with one added figure (figure 9), a shift s->s+1 in the definition of the tree size, and minor correction

Mott-Kondo Insulator Behavior in the Iron Oxychalcogenides

We perform a combined experimental-theoretical study of the Fe-oxychalcogenides (FeO\emph{Ch}) series La$_{2}$O$_{2}$Fe$_{2}$O\emph{M}$_{2}$ (\emph{M}=S, Se), which is the latest among the Fe-based materials with the potential \ to show unconventional high-T$_{c}$ superconductivity (HTSC). A combination of incoherent Hubbard features in X-ray absorption (XAS) and resonant inelastic X-ray scattering (RIXS) spectra, as well as resitivity data, reveal that the parent FeO\emph{Ch} are correlation-driven insulators. To uncover microscopics underlying these findings, we perform local density approximation-plus-dynamical mean field theory (LDA+DMFT) calculations that unravel a Mott-Kondo insulating state. Based upon good agreement between theory and a range of data, we propose that FeO\emph{Ch} may constitute a new, ideal testing ground to explore HTSC arising from a strange metal proximate to a novel selective-Mott quantum criticality

Metal-insulator transition from combined disorder and interaction effects in Hubbard-like electronic lattice models with random hopping

We uncover a disorder-driven instability in the diffusive Fermi liquid phase of a class of many-fermion systems, indicative of a metal-insulator transition of first order type, which arises solely from the competition between quenched disorder and interparticle interactions. Our result is expected to be relevant for sufficiently strong disorder in d = 3 spatial dimensions. Specifically, we study a class of half-filled, Hubbard-like models for spinless fermions with (complex) random hopping and short-ranged interactions on bipartite lattices, in d > 1. In a given realization, the hopping disorder breaks time reversal invariance, but preserves the special ``nesting'' symmetry responsible for the charge density wave instability of the ballistic Fermi liquid. This disorder may arise, e.g., from the application of a random magnetic field to the otherwise clean model. We derive a low energy effective field theory description for this class of disordered, interacting fermion systems, which takes the form of a Finkel'stein non-linear sigma model [A. M. Finkel'stein, Zh. Eksp. Teor. Fiz. 84, 168 (1983), Sov. Phys. JETP 57, 97 (1983)]. We analyze the Finkel'stein sigma model using a perturbative, one-loop renormalization group analysis controlled via an epsilon-expansion in d = 2 + epsilon dimensions. We find that, in d = 2 dimensions, the interactions destabilize the conducting phase known to exist in the disordered, non-interacting system. The metal-insulator transition that we identify in d > 2 dimensions occurs for disorder strengths of order epsilon, and is therefore perturbatively accessible for epsilon << 1. We emphasize that the disordered system has no localized phase in the absence of interactions, so that a localized phase, and the transition into it, can only appear due to the presence of the interactions.Comment: 47 pages, 25 figures; submitted to Phys. Rev. B. Long version of arXiv:cond-mat/060757

Modelling of flow around hexagonal and textured cylinders

The flow regime around a hexagonal polygon with low Reynolds numbers Re<200 is numerically investigated in two different orientations namely face-oriented and corner-oriented. The basic flow characteristics, including drag coefficient, lift coefficient, Strouhal number and critical Reynolds number of the hexagonal cylinders, are calculated using 2D transient numerical analysis. Within the studied range of Re, the predicted lift coefficient and Strouhal number of the face-oriented hexagon were higher than those of the corner-oriented hexagon. In contrast, the predicted drag coefficient and critical Reynolds number of the corner-oriented hexagon were greater than those of the face-oriented. Flow characteristics of a novel textured geometry are also studied using 3D transient analysis. The Strouhal number St of the textured geometry was found to be in between the St of both the hexagonal cylinders, and its lift coefficient is lower than that of the hexagonal cylinders