Kondo lattice on the edge of a two-dimensional topological insulator

We revisit the problem of a single quantum impurity on the edge of a two-dimensional time-reversal invariant topological insulator and show that the zero temperature phase diagram contains a large local moment region for antiferromagnetic Kondo coupling which was missed by previous poor man's scaling treatments. The combination of an exact solution at the so-called decoupling point and a renormalization group analysis \`a la Anderson-Yuval-Hamann allows us to access the regime of strong electron-electron interactions on the edge and strong Kondo coupling. We apply similar methods to the problem of a regular one-dimensional array of quantum impurities interacting with the edge liquid. When the edge electrons are at half-filling with respect to the impurity lattice, the system remains gapless unless the Luttinger parameter of the edge is less than 1/2, in which case two-particle backscattering effects drive the system to a gapped phase with long-range Ising antiferromagnetic order. This is in marked contrast with the gapped disordered ground state of the ordinary half-filled one-dimensional Kondo lattice.Comment: 18 pages, 3 figures; fixed typos, updated reference

Universal crossing probability in anisotropic systems

Scale-invariant universal crossing probabilities are studied for critical anisotropic systems in two dimensions. For weakly anisotropic standard percolation in a rectangular-shaped system, Cardy's exact formula is generalized using a length-rescaling procedure. For strongly anisotropic systems in 1+1 dimensions, exact results are obtained for the random walk with absorbing boundary conditions, which can be considered as a linearized mean-field approximation for directed percolation. The bond and site directed percolation problem is itself studied numerically via Monte Carlo simulations on the diagonal square lattice with either free or periodic boundary conditions. A scale-invariant critical crossing probability is still obtained, which is a universal function of the effective aspect ratio r_eff=c r where r=L/t^z, z is the dynamical exponent and c is a non-universal amplitude.Comment: 7 pages, 4 figure

"The Ising model on spherical lattices: dimer versus Monte Carlo approach"

We study, using dimer and Monte Carlo approaches, the critical properties and finite size effects of the Ising model on honeycomb lattices folded on the tetrahedron. We show that the main critical exponents are not affected by the presence of conical singularities. The finite size scaling of the position of the maxima of the specific heat does not match, however, with the scaling of the correlation length, and the thermodynamic limit is attained faster on the spherical surface than in corresponding lattices on the torus.Comment: 25 pages + 6 figures not included. Latex file. FTUAM 93-2

Local functional models of critical correlations in thin-films

Recent work on local functional theories of critical inhomogeneous fluids and Ising-like magnets has shown them to be a potentially exact, or near exact, description of universal finite-size effects associated with the excess free-energy and scaling of one-point functions in critical thin films. This approach is extended to predict the two-point correlation function G in critical thin-films with symmetric surface fields in arbitrary dimension d. In d=2 we show there is exact agreement with the predictions of conformal invariance for the complete spectrum of correlation lengths as well as the detailed position dependence of the asymptotic decay of G. In d=3 and d>=4 we present new numerical predictions for the universal finite-size correlation length and scaling functions determining the structure of G across the thin-film. Highly accurate analytical closed form expressions for these universal properties are derived in arbitrary dimension.Comment: 4 pages, 1 postscript figure. Submitted to Phys Rev Let

Local renormalization method for random systems

In this paper, we introduce a real-space renormalization transformation for random spin systems on 2D lattices. The general method is formulated for random systems and results from merging two well known real space renormalization techniques, namely the strong disorder renormalization technique (SDRT) and the contractor renormalization (CORE). We analyze the performance of the method on the 2D random transverse field Ising model (RTFIM).Comment: 12 pages, 13 figures. Submitted to the Special Issue on "Quantum Information and Many-Body Theory", New Journal of Physics. Editors: M.B. Plenio, J. Eiser

Droplet shapes on structured substrates and conformal invariance

We consider the finite-size scaling of equilibrium droplet shapes for fluid adsorption (at bulk two-phase co-existence) on heterogeneous substrates and also in wedge geometries in which only a finite domain $\Lambda_{A}$ of the substrate is completely wet. For three-dimensional systems with short-ranged forces we use renormalization group ideas to establish that both the shape of the droplet height and the height-height correlations can be understood from the conformal invariance of an appropriate operator. This allows us to predict the explicit scaling form of the droplet height for a number of different domain shapes. For systems with long-ranged forces, conformal invariance is not obeyed but the droplet shape is still shown to exhibit strong scaling behaviour. We argue that droplet formation in heterogeneous wedge geometries also shows a number of different scaling regimes depending on the range of the forces. The conformal invariance of the wedge droplet shape for short-ranged forces is shown explicitly.Comment: 20 pages, 7 figures. (Submitted to J.Phys.:Cond.Mat.

Finite-size scaling and conformal anomaly of the Ising model in curved space

We study the finite-size scaling of the free energy of the Ising model on lattices with the topology of the tetrahedron and the octahedron. Our construction allows to perform changes in the length scale of the model without altering the distribution of the curvature in the space. We show that the subleading contribution to the free energy follows a logarithmic dependence, in agreement with the conformal field theory prediction. The conformal anomaly is given by the sum of the contributions computed at each of the conical singularities of the space, except when perfect order of the spins is precluded by frustration in the model.Comment: 4 pages, 4 Postscript figure

Quasi-2D Confinement of a BEC in a Combined Optical and Magnetic Potential

We have added an optical potential to a conventional Time-averaged Orbiting Potential (TOP) trap to create a highly anisotropic hybrid trap for ultracold atoms. Axial confinement is provided by the optical potential; the maximum frequency currently obtainable in this direction is 2.2 kHz for rubidium. The radial confinement is independently controlled by the magnetic trap and can be a factor of 700 times smaller than in the axial direction. This large anisotropy is more than sufficient to confine condensates with ~10^5 atoms in a Quasi-2D (Q2D) regime, and we have verified this by measuring a change in the free expansion of the condensate; our results agree with a variational model.Comment: 11 pages, 10 figur

Bekenstein entropy bound for weakly-coupled field theories on a 3-sphere

We calculate the high temperature partition functions for SU(Nc) or U(Nc) gauge theories in the deconfined phase on S^1 x S^3, with scalars, vectors, and/or fermions in an arbitrary representation, at zero 't Hooft coupling and large Nc, using analytical methods. We compare these with numerical results which are also valid in the low temperature limit and show that the Bekenstein entropy bound resulting from the partition functions for theories with any amount of massless scalar, fermionic, and/or vector matter is always satisfied when the zero-point contribution is included, while the theory is sufficiently far from a phase transition. We further consider the effect of adding massive scalar or fermionic matter and show that the Bekenstein bound is satisfied when the Casimir energy is regularized under the constraint that it vanishes in the large mass limit. These calculations can be generalized straightforwardly for the case of a different number of spatial dimensions.Comment: 32 pages, 12 figures. v2: Clarifications added. JHEP versio

Logarithmic Corrections for Spin Glasses, Percolation and Lee-Yang Singularities in Six Dimensions

We study analytically the logarithmic corrections to the critical exponents of the critical behavior of correlation length, susceptibility and specific heat for the temperature and the finite-size scaling behavior, for a generic $\phi^3$ theory at its upper critical dimension (six). We have also computed the leading correction to scaling as a function of the lattice size. We distinguish the obtained formulas to the following special cases: percolation, Lee-Yang (LY) singularities and $m$-component spin glasses. We have compared our results for the Ising spin glass case with numerical simulations finding a very good agreement. Finally, and using the results obtained for the Lee-Yang singularities in six dimensions, we have computed the logarithmic corrections to the singular part of the free energy for lattice animals in eight dimensions.Comment: 18 pages. We have extended the computation to lattice animals in eight dimensions. To be published in Journal of Physics