2d random Dirac fermions: large N approach

We study the symmetry classes for the random Dirac fermions in 2 dimensions. We consider $N_f$ species of fermions, coupled by different types of disorder. We analyse the renormalisation group flow at the order of one loop. At $N_f$ large, the disorder distribution flows to an isotropic distribution and the effective action is a sigma model.Comment: 12 pages, contribution to the proceedings of Advanced NATO Workshop on Statistical Field Theories, Como, June 18-23, 200

Eigenvectors and scalar products for long range interacting spin chains II: the finite size effects

In this note, we study the eigenvectors and the scalar products the integrable long-range deformation of a XXX spin chain which is solved exactly by algebraic Bethe ansatz, and it coincides in the bulk with the Inozemtsev spin chain. At the closing point it contains a defect which effectively removes the wrapping interactions. Here we concentrate on determining the defect term for the first non-trivial order in perturbation in the deformation parameter and how it affects the Bethe ansatz equations. Our study is motivated by the relation with the dilatation operator of the N = 4 gauge theory in the su(2) sector.Comment: 11 pages, no figure; some misprints correcte

Planar N=4 gauge theory and the Inozemtsev long range spin chain

We investigate whether the (planar, two complex scalar) dilatation operator of N=4 gauge theory can be, perturbatively and, perhaps, non-perturbatively, described by an integrable long range spin chain with elliptic exchange interaction. Such a chain was introduced some time ago by Inozemtsev. In the limit of sufficiently ``long'' operators a Bethe ansatz exists, which we apply at the perturbative two- and three-loop level. Spectacular agreement is found with spinning string predictions of Frolov and Tseytlin for the two-loop energies of certain large charge operators. However, we then go on to show that the agreement between perturbative gauge theory and semi-classical string theory begins to break down, in a subtle fashion, at the three-loop level. This corroborates a recently found disagreement between three-loop gauge theory and near plane-wave string theory results, and quantitatively explains a previously obtained puzzling deviation between the string proposal and a numerical extrapolation of finite size three-loop anomalous dimensions. At four loops and beyond, we find that the Inozemtsev chain exhibits a generic breakdown of perturbative BMN scaling. However, our proposal is not necessarily limited to perturbation theory, and one would hope that the string theory results can be recovered from the Inozemtsev chain at strong 't Hooft coupling.Comment: 31 pages, no figure; v1: one reference added, minor changes; v2: slightly extended discussion of rapidity, references adde

A One Dimensional Ideal Gas of Spinons, or Some Exact Results on the XXX Spin Chain with Long Range Interaction

We describe a few properties of the XXX spin chain with long range interaction. The plan of these notes is: 1. The Hamiltonian 2. Symmetry of the model 3. The irreducible multiplets 4. The spectrum 5. Wave functions and statistics 6. The spinon description 7. The thermodynamicsComment: Latex. Talk given by the first author at the Cargese-1993 workshop "Strings, conformal models and Topological felds theorie

Dynamic Graphs on the GPU

We present a fast dynamic graph data structure for the GPU. Our dynamic graph structure uses one hash table per vertex to store adjacency lists and achieves 3.4–14.8x faster insertion rates over the state of the art across a diverse set of large datasets, as well as deletion speedups up to 7.8x. The data structure supports queries and dynamic updates through both edge and vertex insertion and deletion. In addition, we define a comprehensive evaluation strategy based on operations, workloads, and applications that we believe better characterize and evaluate dynamic graph data structures