Crumpling transition of the triangular lattice without open edges: effect of a modified folding rule

Folding of the triangular lattice in a discrete three-dimensional space is investigated by means of the transfer-matrix method. This model was introduced by Bowick and co-workers as a discretized version of the polymerized membrane in thermal equilibrium. The folding rule (constraint) is incompatible with the periodic-boundary condition, and the simulation has been made under the open-boundary condition. In this paper, we propose a modified constraint, which is compatible with the periodic-boundary condition; technically, the restoration of translational invariance leads to a substantial reduction of the transfer-matrix size. Treating the cluster sizes L \le 7, we analyze the singularities of the crumpling transitions for a wide range of the bending rigidity K. We observe a series of the crumpling transitions at K=0.206(2), -0.32(1), and -0.76(10). At each transition point, we estimate the latent heat as Q=0.356(30), 0.08(3), and 0.05(5), respectively

Folding of the triangular lattice in a discrete three-dimensional space: Crumpling transitions in the negative-bending-rigidity regime

Folding of the triangular lattice in a discrete three-dimensional space is studied numerically. Such ``discrete folding'' was introduced by Bowick and co-workers as a simplified version of the polymerized membrane in thermal equilibrium. According to their cluster-variation method (CVM) analysis, there appear various types of phases as the bending rigidity K changes in the range -infty < K < infty. In this paper, we investigate the K<0 regime, for which the CVM analysis with the single-hexagon-cluster approximation predicts two types of (crumpling) transitions of both continuous and discontinuous characters. We diagonalized the transfer matrix for the strip widths up to L=26 with the aid of the density-matrix renormalization group. Thereby, we found that discontinuous transitions occur successively at K=-0.76(1) and -0.32(1). Actually, these transitions are accompanied with distinct hysteresis effects. On the contrary, the latent-heat releases are suppressed considerably as Q=0.03(2) and 0.04(2) for respective transitions. These results indicate that the singularity of crumpling transition can turn into a weak-first-order type by appreciating the fluctuations beyond a meanfield level

Non-Hermitian Luttinger Liquids and Vortex Physics

As a model of two thermally excited flux liquids connected by a weak link, we study the effect of a single line defect on vortex filaments oriented parallel to the surface of a thin planar superconductor. When the applied field is tilted relative to the line defect, the physics is described by a nonhermitian Luttinger liquid of interacting quantum bosons in one spatial dimension with a point defect. We analyze this problem using a combination of analytic and numerical density matrix renormalization group methods, uncovering a delicate interplay between enhancement of pinning due to Luttinger liquid effects and depinning due to the tilted magnetic field. Interactions dramatically improve the ability of a single columnar pin to suppress vortex tilt when the Luttinger liquid parameter g is less than or equal to one.Comment: 4 pages, 5 eps figures, minor changes made, one reference adde

Free Energies of Isolated 5- and 7-fold Disclinations in Hexatic Membranes

We examine the shapes and energies of 5- and 7-fold disclinations in low-temperature hexatic membranes. These defects buckle at different values of the ratio of the bending rigidity, $\kappa$, to the hexatic stiffness constant, $K_A$, suggesting {\em two} distinct Kosterlitz-Thouless defect proliferation temperatures. Seven-fold disclinations are studied in detail numerically for arbitrary $\kappa/K_A$. We argue that thermal fluctuations always drive $\kappa/K_A$ into an ``unbuckled'' regime at long wavelengths, so that disclinations should, in fact, proliferate at the {\em same} critical temperature. We show analytically that both types of defects have power law shapes with continuously variable exponents in the ``unbuckled'' regime. Thermal fluctuations then lock in specific power laws at long wavelengths, which we calculate for 5- and 7-fold defects at low temperatures.Comment: LaTeX format. 17 pages. To appear in Phys. Rev.

Efficiency of thin film photocells

We propose a new concept for the design of high-efficiency photocells based on ultra-thin (submicron) semiconductor films of controlled thickness. Using a microscopic model of a thin dielectric layer interacting with incident electromagnetic radiation we evaluate the efficiency of conversion of solar radiation into the electric power. We determine the optimal range of parameters which maximize the efficiency of such photovoltaic element.Comment: 5 pages, 3 figure

The generalized Fenyes-Nelson model for free scalar field theory

The generalized Fenyes--Nelson model of quantum mechanics is applied to the free scalar field. The resulting Markov field is equivalent to the Euclidean Markov field with the times scaled by a common factor which depends on the diffusion parameter. This result is consistent between Guerra's earlier work on stochastic quantization of scalar fields. It suggests a deep connection between Euclidean field theory and the stochastic interpretation of quantum mechanics. The question of Lorentz covariance is also discussed.Comment: 6 page

Boundary-detection algorithm for locating edges in digital imagery

The author has identified the following significant results. Initial development of a computer program which implements a boundary detection algorithm to detect edges in digital images is described. An evaluation of the boundary detection algorithm was conducted to locate boundaries of lakes from LANDSAT-1 imagery. The accuracy of the boundary detection algorithm was determined by comparing the area within boundaries of lakes located using digitized LANDSAT imagery with the area of the same lakes planimetered from imagery collected from an aircraft platform

Self-Consistent Screening Approximation for Flexible Membranes: Application to Graphene

Crystalline membranes at finite temperatures have an anomalous behavior of the bending rigidity that makes them more rigid in the long wavelength limit. This issue is particularly relevant for applications of graphene in nano- and micro-electromechanical systems. We calculate numerically the height-height correlation function $G(q)$ of crystalline two-dimensional membranes, determining the renormalized bending rigidity, in the range of wavevectors $q$ from $10^{-7}$ \AA$^{-1}$ till 10 \AA$^{-1}$ in the self-consistent screening approximation (SCSA). For parameters appropriate to graphene, the calculated correlation function agrees reasonably with the results of atomistic Monte Carlo simulations for this material within the range of $q$ from $10^{-2}$ \AA$^{-1}$ till 1 \AA$^{-1}$. In the limit $q\rightarrow 0$ our data for the exponent $\eta$ of the renormalized bending rigidity $\kappa_R(q)\propto q^{-\eta}$ is compatible with the previously known analytical results for the SCSA $\eta\simeq 0.82$. However, this limit appears to be reached only for $q<10^{-5}$ \AA$^{-1}$ whereas at intermediate $q$ the behavior of $G(q)$ cannot be described by a single exponent.Comment: 5 pages, 4 figure

Coarsening in potential and nonpotential models of oblique stripe patterns

We study the coarsening of two-dimensional oblique stripe patterns by numerically solving potential and nonpotential anisotropic Swift-Hohenberg equations. Close to onset, all models exhibit isotropic coarsening with a single characteristic length scale growing in time as $t^{1/2}$. Further from onset, the characteristic lengths along the preferred directions $\hat{x}$ and $\hat{y}$ grow with different exponents, close to 1/3 and 1/2, respectively. In this regime, one-dimensional dynamical scaling relations hold. We draw an analogy between this problem and Model A in a stationary, modulated external field. For deep quenches, nonpotential effects produce a complicated dislocation dynamics that can lead to either arrested or faster-than-power-law growth, depending on the model considered. In the arrested case, small isolated domains shrink down to a finite size and fail to disappear. A comparison with available experimental results of electroconvection in nematics is presented.Comment: 13 pages, 13 figures. To appear in Phys. Rev.