Multicriticality of the (2+1)-dimensional gonihedric model: A realization of the (d,m)=(3,2) Lifshitz point

Multicriticality of the gonihedric model in 2+1 dimensions is investigated numerically. The gonihedric model is a fully frustrated Ising magnet with the finely tuned plaquette-type (four-body and plaquette-diagonal) interactions, which cancel out the domain-wall surface tension. Because the quantum-mechanical fluctuation along the imaginary-time direction is simply ferromagnetic, the criticality of the (2+1)-dimensional gonihedric model should be an anisotropic one; that is, the respective critical indices of real-space (\perp) and imaginary-time (\parallel) sectors do not coincide. Extending the parameter space to control the domain-wall surface tension, we analyze the criticality in terms of the crossover (multicritical) scaling theory. By means of the numerical diagonalization for the clusters with N\le 28 spins, we obtained the correlation-length critical indices (\nu_\perp,\nu_\parallel)=(0.45(10),1.04(27)), and the crossover exponent \phi=0.7(2). Our results are comparable to (\nu_{\perp},\nu_{\parallel})=(0.482,1.230), and \phi=0.688 obtained by Diehl and Shpot for the (d,m)=(3,2) Lifshitz point with the \epsilon-expansion method up to O(\epsilon^2)

A new description of motion of the Fermionic SO(2N+2) top in the classical limit under the quasi-anticommutation relation approximation

The boson images of fermion SO(2N+1) Lie operators have been given together with those of SO(2N+2) ones. The SO(2N+1) Lie operators are generators of rotation in the (2N+1)-dimensional Euclidian space (N: number of single-particle states of the fermions). The images of fermion annihilation-creation operators must satisfy the canonical anti-commutation relations, when they operate on a spinor subspace. In the regular representation space we use a boson Hamiltonian with Lagrange multipliers to select out the spinor subspace. Based on these facts, a new description of a fermionic SO(2N+2) top is proposed. From the Heisenberg equations of motions for the boson operators, we get the SO(2N+1) self-consistent field (SCF) Hartree-Bogoliubov (HB) equation for the classical stationary motion of the fermion top. Decomposing an SO(2N+1) matrix into matrices describing paired and unpaired modes of fermions, we obtain a new form of the SO(2N+1) SCF equation with respect to the paired-mode amplitudes. To demonstrate the effectiveness of the new description based on the bosonization theory, the extended HB eigenvalue equation is applied to a superconducting toy-model which consists of a particle-hole plus BCS type interaction. It is solved to reach an interesting and exciting solution which is not found in the traditional HB eigenvalue equation, due to the unpaired-mode effects. To complete the new description, the Lagrange multipliers must be determined in the classical limit. For this aim a quasi anti-commutation-relation approximation is proposed. Only if a certain relation between an SO(2N+1) parameter z and the N is satisfied, unknown parameters k and l in the Lagrange multipliers can be determined withuout any inconcistency.Comment: 36 pages, no figures, typos corrected, published versio

Conductivity of a graphene strip: width and gate-voltage dependencies

We study the conductivity of a graphene strip taking into account electrostatically-induced charge accumulation on its edges. Using a local dependency of the conductivity on the carrier concentration we find that the electrostatic size effect in doped graphene strip of the width of 0.5 - 3 $\mu$m can result in a significant (about 40%) enhancement of the effective conductivity in comparison to the infinitely wide samples. This effect should be taken into account both in the device simulation as well as for verification of scattering mechanisms in graphene.Comment: 3 pages, 4 figure

Direct observation of the effective bending moduli of a fluid membrane: Free-energy cost due to the reference-plane deformations

Effective bending moduli of a fluid membrane are investigated by means of the transfer-matrix method developed in our preceding paper. This method allows us to survey various statistical measures for the partition sum. The role of the statistical measures is arousing much attention, since Pinnow and Helfrich claimed that under a suitable statistical measure, that is, the local mean curvature, the fluid membranes are stiffened, rather than softened, by thermal undulations. In this paper, we propose an efficient method to observe the effective bending moduli directly: We subjected a fluid membrane to a curved reference plane, and from the free-energy cost due to the reference-plane deformations, we read off the effective bending moduli. Accepting the mean-curvature measure, we found that the effective bending rigidity gains even in the case of very flexible membrane (small bare rigidity); it has been rather controversial that for such non-perturbative regime, the analytical prediction does apply. We also incorporate the Gaussian-curvature modulus, and calculated its effective rigidity. Thereby, we found that the effective Gaussian-curvature modulus stays almost scale-invariant. All these features are contrasted with the results under the normal-displacement measure

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

Transfer-matrix approach to the three-dimensional bond percolation: An application of Novotny's formalism

A transfer-matrix simulation scheme for the three-dimensional (d=3) bond percolation is presented. Our scheme is based on Novotny's transfer-matrix formalism, which enables us to consider arbitrary (integral) number of sites N constituting a unit of the transfer-matrix slice even for d=3. Such an arbitrariness allows us to perform systematic finite-size-scaling analysis of the criticality at the percolation threshold. Diagonalizing the transfer matrix for N =4,5,...,10, we obtain an estimate for the correlation-length critical exponent nu = 0.81(5)

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

Near-Infrared Counterparts to Chandra X-ray Sources toward the Galactic Center. I. Statistics and a Catalog of Candidates

We present a catalog of 5184 candidate infrared counterparts to X-ray sources detected towards the Galactic center. The X-ray sample contains 9017 point sources detected in this region by the Chandra X-ray Observatory, including data from a recent deep survey of the central 2 x 0.8 deg of the Galactic plane. A total of 6760 of these sources have hard X-ray colors, and the majority of them lie near the Galactic center, while most of the remaining 2257 soft X-ray sources lie in the foreground. We cross-correlated the X-ray source positions with the 2MASS and SIRIUS near-infrared catalogs, which collectively contain stars with a 10-sigma limiting flux of K_s<=15.6 mag. In order to distinguish absorbed infrared sources near the Galactic center from those in the foreground, we defined red and blue sources as those which have H-K_s>=0.9 and <=0.9 mag, respectively. We find that 5.8(1.5)% of the hard X-ray sources have real infrared counterparts, of which 228(99) are red and 166(27) are blue. The red counterparts are probably comprised of WR/O stars, HMXBs, and symbiotics near the Galactic center. We also find that 39.4(1.0)% of the soft X-ray sources have blue infrared counterparts; most of these are probably coronally active dwarfs in the foreground. There is a noteworthy collection of ~20 red counterparts to hard X-ray sources near the Sagittarius-B H II region, which are probably massive binaries that have formed within the last several Myr. For each of the infrared matches to X-ray sources in our catalog we derived the probability that the association is real, based on the results of the cross-correlation analysis. The catalog will serve spectroscopic surveys to identify infrared counterparts to X-ray sources near the Galactic center.Comment: Submitted to ApJ January 16, 2009; accepted July 21, 2009; 30 pages, 6 figure

Pressure-induced amorphization, crystal-crystal transformations and the memory glass effect in interacting particles in two dimensions

We study a model of interacting particles in two dimensions to address the relation between crystal-crystal transformations and pressure-induced amorphization. On increasing pressure at very low temperature, our model undergoes a martensitic crystal-crystal transformation. The characteristics of the resulting polycrystalline structure depend on defect density, compression rate, and nucleation and growth barriers. We find two different limiting cases. In one of them the martensite crystals, once nucleated, grow easily perpendicularly to the invariant interface, and the final structure contains large crystals of the different martensite variants. Upon decompression almost every atom returns to its original position, and the original crystal is fully recovered. In the second limiting case, after nucleation the growth of martensite crystals is inhibited by energetic barriers. The final morphology in this case is that of a polycrystal with a very small crystal size. This may be taken to be amorphous if we have only access (as experimentally may be the case) to the angularly averaged structure factor. However, this `X-ray amorphous' material is anisotropic, and this shows up upon decompression, when it recovers the original crystalline structure with an orientation correlated with the one it had prior to compression. The memory effect of this X-ray amorphous material is a natural consequence of the memory effect associated to the underlying martensitic transformation. We suggest that this kind of mechanism is present in many of the experimental observations of the memory glass effect, in which a crystal with the original orientation is recovered from an apparently amorphous sample when pressure is released.Comment: 13 pages, 13 figures, to be published in Phys. Rev.

Nanostructure of cellulose microfibrils in spruce wood

The structure of cellulose microfibrils in wood is not known in detail, despite the abundance of cellulose in woody biomass and its importance for biology, energy, and engineering. The structure of the microfibrils of spruce wood cellulose was investigated using a range of spectroscopic methods coupled to small-angle neutron and wide-angle X-ray scattering. The scattering data were consistent with 24-chain microfibrils and favored a “rectangular” model with both hydrophobic and hydrophilic surfaces exposed. Disorder in chain packing and hydrogen bonding was shown to increase outwards from the microfibril center. The extent of disorder blurred the distinction between the I alpha and I beta allomorphs. Chains at the surface were distinct in conformation, with high levels of conformational disorder at C-6, less intramolecular hydrogen bonding and more outward-directed hydrogen bonding. Axial disorder could be explained in terms of twisting of the microfibrils, with implications for their biosynthesis