Holographic Entropy on the Brane in de Sitter Schwarzschild Space

The relationship between the entropy of de Sitter (dS) Schwarzschild space and that of the CFT, which lives on the brane, is discussed by using Friedmann-Robertson-Walker (FRW) equations and Cardy-Verlinde formula. The cosmological constant appears on the brane with time-like metric in dS Schwarzschild background. On the other hand, in case of the brane with space-like metric in dS Schwarzschild background, the cosmological constant of the brane does not appear because we can choose brane tension to cancel it. We show that when the brane crosses the horizon of dS Schwarzschild black hole, both for time-like and space-like cases, the entropy of the CFT exactly agrees with the black hole entropy of 5-dimensional AdS Schwarzschild background as it happens in the AdS/CFT correspondence.Comment: 8 pages, LaTeX, Referneces adde

Critical behaviour in parabolic geometries

We study two-dimensional systems with boundary curves described by power laws. Using conformal mappings we obtain the correlations at the bulk critical point. Three different classes of behaviour are found and explained by scaling arguments which also apply to higher dimensions. For an Ising system of parabolic shape the behaviour of the order at the tip is also found.Comment: Old paper, for archiving. 6 pages, 1 figure, epsf, IOP macr

A supersymmetric multicritical point in a model of lattice fermions

We study a model of spinless fermions with infinite nearest-neighbor repulsion on the square ladder which has microscopic supersymmetry. It has been conjectured that in the continuum the model is described by the superconformal minimal model with central charge c=3/2. Thus far it has not been possible to confirm this conjecture due to strong finite-size corrections in numerical data. We trace the origin of these corrections to the presence of unusual marginal operators that break Lorentz invariance, but preserve part of the supersymmetry. By relying mostly on entanglement entropy calculations with the density-matrix renormalization group, we are able to reduce finite-size effects significantly. This allows us to unambiguously determine the continuum theory of the model. We also study perturbations of the model and establish that the supersymmetric model is a multicritical point. Our work underlines the power of entanglement entropy as a probe of the phases of quantum many-body systems.Comment: 16 pages, 8 figure

Local defect in a magnet with long-range interactions

We investigate a single defect coupling to the square of the order parameter in a nearly critical magnet with long-range spatial interactions of the form $r^{-(d+\sigma)}$, focusing on magnetic droplets nucleated at the defect while the bulk system is in the paramagnetic phase. Because of the long-range interaction, the droplet develops a power-law tail which is energetically unfavorable. However, as long as $\sigma>0$, the tail contribution to the droplet free energy is subleading in the limit of large droplets; and the free energy becomes identical to the case of short-range interactions. We also study the droplet quantum dynamics with and without dissipation; and we discuss the consequences of our results for defects in itinerant quantum ferromagnets.Comment: 8 pages, 5 eps figures, final version, as publishe

Critical phenomena and quantum phase transition in long range Heisenberg antiferromagnetic chains

Antiferromagnetic Hamiltonians with short-range, non-frustrating interactions are well-known to exhibit long range magnetic order in dimensions, $d\geq 2$ but exhibit only quasi long range order, with power law decay of correlations, in d=1 (for half-integer spin). On the other hand, non-frustrating long range interactions can induce long range order in d=1. We study Hamiltonians in which the long range interactions have an adjustable amplitude lambda, as well as an adjustable power-law $1/|x|^\alpha$, using a combination of quantum Monte Carlo and analytic methods: spin-wave, large-N non-linear sigma model, and renormalization group methods. We map out the phase diagram in the lambda-alpha plane and study the nature of the critical line separating the phases with long range and quasi long range order. We find that this corresponds to a novel line of critical points with continuously varying critical exponents and a dynamical exponent, z<1.Comment: 27 pages, 12 figures. RG flow added. Final version to appear in JSTA

Fermionic field theory for directed percolation in (1+1) dimensions

We formulate directed percolation in (1+1) dimensions in the language of a reaction-diffusion process with exclusion taking place in one space dimension. We map the master equation that describes the dynamics of the system onto a quantum spin chain problem. From there we build an interacting fermionic field theory of a new type. We study the resulting theory using renormalization group techniques. This yields numerical estimates for the critical exponents and provides a new alternative analytic systematic procedure to study low-dimensional directed percolation.Comment: 20 pages, 2 figure

Long-range epidemic spreading with immunization

We study the phase transition between survival and extinction in an epidemic process with long-range interactions and immunization. This model can be viewed as the well-known general epidemic process (GEP) in which nearest-neighbor interactions are replaced by Levy flights over distances r which are distributed as P(r) ~ r^(-d-sigma). By extensive numerical simulations we confirm previous field-theoretical results obtained by Janssen et al. [Eur. Phys. J. B7, 137 (1999)].Comment: LaTeX, 14 pages, 4 eps figure

Frustration of decoherence in YY-shaped superconducting Josephson networks

We examine the possibility that pertinent impurities in a condensed matter system may help in designing quantum devices with enhanced coherent behaviors. For this purpose, we analyze a field theory model describing Y- shaped superconducting Josephson networks. We show that a new finite coupling stable infrared fixed point emerges in its phase diagram; we then explicitly evidence that, when engineered to operate near by this new fixed point, Y-shaped networks support two-level quantum systems, for which the entanglement with the environment is frustrated. We briefly address the potential relevance of this result for engineering finite-size superconducting devices with enhanced quantum coherence. Our approach uses boundary conformal field theory since it naturally allows for a field-theoretical treatment of the phase slips (instantons), describing the quantum tunneling between degenerate levels.Comment: 11 pages, 5 .eps figures; several changes in the presentation and in the figures, upgraded reference

Large-scale anisotropy in scalar turbulence

The effect of anisotropy on the statistics of a passive tracer transported by a turbulent flow is investigated. We show that under broad conditions an arbitrarily small amount of anisotropy propagates to the large scales where it eventually dominates the structure of the concentration field. This result is obtained analytically in the framework of an exactly solvable model and confirmed by numerical simulations of scalar transport in two-dimensional turbulence

Lifshitz-like systems and AdS null deformations

Following arXiv:1005.3291 [hep-th], we discuss certain lightlike deformations of $AdS_5\times X^5$ in Type IIB string theory sourced by a lightlike dilaton $\Phi(x^+)$ dual to the N=4 super Yang-Mills theory with a lightlike varying gauge coupling. We argue that in the case where the $x^+$-direction is noncompact, these solutions describe anisotropic 3+1-dim Lifshitz-like systems with a potential in the $x^+$-direction generated by the lightlike dilaton. We then describe solutions of this sort with a linear dilaton. This enables a detailed calculation of 2-point correlation functions of operators dual to bulk scalars and helps illustrate the spatial structure of these theories. Following this, we discuss a nongeometric string construction involving a compactification along the $x^+$-direction of this linear dilaton system. We also point out similar IIB axionic solutions. Similar bulk arguments for $x^+$-noncompact can be carried out for deformations of $AdS_4\times X^7$ in M-theory.Comment: Latex, 20pgs, 1 eps fig; v2. references added; v3. minor clarifications added, to appear in PR