Finite-size-scaling analysis of the XY universality class between two and three dimensions: An application of Novotny's transfer-matrix method

Based on Novotny's transfer-matrix method, we simulated the (stacked) triangular Ising antiferromagnet embedded in the space with the dimensions variable in the range 2 \le d \le 3. Our aim is to investigate the criticality of the XY universality class for 2 \le d \le 3. For that purpose, we employed an extended version of the finite-size-scaling analysis developed by Novotny, who utilized this scheme to survey the Ising criticality (ferromagnet) for 1 \le d \le 3. Diagonalizing the transfer matrix for the system sizes N up to N=17, we calculated the $d$-dependent correlation-length critical exponent \nu(d). Our simulation result \nu(d) appears to interpolate smoothly the known two limiting cases, namely, the KT and d=3 XY universality classes, and the intermediate behavior bears close resemblance to that of the analytical formula via the 1/N-expansion technique. Methodological details including the modifications specific to the present model are reported

Comment on ``Density Matrix Renormalization Group Study of the Haldane Phase in Random One-Dimensional Antiferromagnets"

In a recent Letter (PRL 83, 3297 (1999)), Hida presented numerical results indicating that the Haldane phase of the Heisenberg antiferromagnetic spin-1 chain is stable against bond randomness, for box distributions of the bond strength, even when the box distribution stretches to zero bond strength. The author thus concluded that the Haldane phase is stable against bond randomness for any distribution of the bond strength, no matter how broad. In this Comment, we (i) point out that the randomness distributions studied in this Letter do not represent the broadest possible distributions, and therefore these numerical results do not lead to the conclusion that the Haldane phase is stable against any randomness; and (ii) provide a semiquantitative estimate of the critical randomness beyond which the Haldane phase yields to the Random Singlet phase, in a specific class of random distribution functions for the bond strength.Comment: A comment on PRL 83, 3297 (1999). One pag

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

Time Dependent Pairing Equations for Seniority One Nuclear Systems

When the time dependent Hartree-Fock-Bogoliubov intrinsic equations of motion are solved in the case of seniority one nuclear systems, the unpaired nucleon remains on the same orbital. The blocking effect hinders the possibility to skip from one orbital to another. This unpleasant feature is by-passed with a new set of pairing time dependent equations that allows the possibility that the unpaired nucleon changes its single-particle level. These equations generalize the time dependent Hartree-Fock-Bogoliubov equations of motion by including the Landau-Zener effect. The derivation of these new equations is presented in details. These equations are applied in the case of a superasymmetric fission process, that is, in order to explain the fine structure the 14C emission from 233Ra. A new version of the Woods-Saxon model extended for two-center potentials is used in this context.Comment: 12 pages, 6 figure

Construction of an isotropic cellular automaton for a reaction-diffusion equation by means of a random walk

We propose a new method to construct an isotropic cellular automaton corresponding to a reaction-diffusion equation. The method consists of replacing the diffusion term and the reaction term of the reaction-diffusion equation with a random walk of microscopic particles and a discrete vector field which defines the time evolution of the particles. The cellular automaton thus obtained can retain isotropy and therefore reproduces the patterns found in the numerical solutions of the reaction-diffusion equation. As a specific example, we apply the method to the Belousov-Zhabotinsky reaction in excitable media

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)

High resolution observations of Cen A: Yellow and red supergiants in a region of jet-induced star formation?

We present the analysis of near infrared (NIR), adaptive optics (AO) Subaru and archived HST imaging data of a region near the northern middle lobe (NML) of the Centaurus A (Cen A) jet, at a distance of $\sim15$ kpc north-east (NE) from the center of NGC5128. Low-pass filtering of the NIR images reveals strong -- $>3\sigma$ above the background mean -- signal at the expected position of the brightest star in the equivalent HST field. Statistical analysis of the NIR background noise suggests that the probability to observe $>3\sigma$ signal at the same position, in three independent measurements due to stochastic background fluctuations alone is negligible ($\leq10^{-7}\%$) and, therefore, that this signal should reflect the detection of the NIR counterparts of the brightest HST star. An extensive photometric analysis of this star yields $V-I$, visual-NIR, and NIR colors expected from a yellow supergiant (YSG) with an estimated age $\sim10^{+4}_{-3}$ Myr. Furthermore, the second and third brighter HST stars are, likely, also supergiants in Cen A, with estimated ages $\sim16^{+6}_{-3}$ Myr and $\sim25^{+15}_{-9}$ Myr, respectively. The ages of these three supergiants are in good agreement with the ages of the young massive stars that were previously found in the vicinity and are thought to have formed during the later phases of the jet-HI cloud interaction that appears to drive the star formation (SF) in the region for the past $\sim100$ Myr.Comment: 11 pages, 6 figures, 2 tables, accepted for publication in Ap

Scaling Theory of Antiferromagnetic Heisenberg Ladder Models

The $S=1/2$ antiferromagnetic Heisenberg model on multi-leg ladders is investigated. Criticality of the ground-state transition is explored by means of finite-size scaling. The ladders with an even number of legs and those with an odd number of legs are distinguished clearly. In the former, the energy gap opens up as $\Delta E\sim{J_\perp}$, where ${J_\perp}$ is the strength of the antiferromagnetic inter-chain coupling. In the latter, the critical phase with the central charge $c=1$ extends over the whole region of ${J_\perp}>0$.Comment: 12 pages with 9 Postscript figures. To appear in J. Phys. A: Math. Ge

Ricardian Equivalence Under Asymmetric Information

Several empirical studies have found that extended household units do not appear to be highly altruistically linked, thereby violating the very premise of the Ricardian Equivalence Hypothesis (REH). This finding has a very strong implication for the effectiveness of fiscal policies that change the allocation of resources between generations. We build a two-sided altruistic-linkage model in which private transfers are made in the presence of two types of shocks: an “observable” shock that is public information (for example, a public redistribution like debt or pay-as-you-go social security) and an “unobservable” shock that is private information (for example, individual wage innovations). Parents and children observe each other’s total income but not each other’s effort level. In the second-best solution, unobservable shocks are only partially shared, whereas, for any utility function satisfying a condition derived herein, observable shocks are fully shared. The model, therefore, can generate the low degree of risk sharing found in previous empirical studies, but REH still holds