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

Superconductivity of the Ternary Boride Li_2Pd_3B Probed by ^{11}B NMR

We report a ^{11}B NMR measurement on the recently discovered superconductor Li_2Pd_3B. The nuclear spin lattice relaxation rate 1/T_1 shows a well-defined coherence peak just below T_c (H=1.46 T)=5.7 K, and the spin susceptibility measured by the Knight shift also decreases below T_c. These results indicate that the superconductivity is of conventional nature, with an isotropic gap. Our results also suggest that the $p$-electrons of boron and the d-electrons of palladium that hybridize with boron $p$-electrons are primarily responsible for the superconductivity.Comment: 4 pages, 5 figure

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

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

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

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

VHE Observations of BL Lacertae Objects: 1995-2000

The results of observations of 29 BL Lacertae objects taken with the Whipple Observatory 10 m gamma-ray Telescope between 1995 and 2000 are presented.Comment: 4 pages to be published in the Proceedings of the 28th International Cosmic Ray Conference (Tsukuba, Japan 2003

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)

Quantum-fluctuation-induced collisions and subsequent excitation gap of an elastic string between walls

An elastic string embedded between rigid walls is simulated by means of the density-matrix renormalization group. The string collides against the walls owing to the quantum-mechanical zero-point fluctuations. Such ``quantum entropic'' interaction has come under thorough theoretical investigation in the context of the stripe phase observed experimentally in doped cuprates. We found that the excitation gap opens in the form of exponential singularity DeltaE ~ exp(-Ad^sigma) (d: wall spacing) with the exponent sigma =0.6(3), which is substantially smaller than the meanfield value sigma=2. That is, the excitation gap is much larger than that anticipated from meanfield, suggesting that the string is subjected to robust pinning potential due to the quantum collisions. This feature supports Zaanen's ``order out of disorder'' mechanism which would be responsible to the stabilization of the stripe phase

A Cluster of Class I/f/II YSOs Discovered Near the Cepheid SU Cas

Preliminary constraints are placed on a cluster of YSOs (J2000 02:54:31.4 +69:20:32.5) discovered in the field of the classical Cepheid SU Cas. WISE 3.4, 4.6, 12, and 22 um images reveal that the cluster deviates from spherical symmetry and exhibits an apparent diameter of 3x6'. SEDs constructed using 2MASS Ks (2.2 um) and WISE photometry indicate that 19 (36%) class I, 21 (40%) class f, and 13 (25%) class II objects lie r<3' from the cluster center. Conversely, 11 (18%) class I, 13 (21%) class f, and 37 (61%) class II objects were detected for r>3'. Approximately 50% of the class I sources within r<3' were classified solely using WISE photometry owing to the absence of detections by 2MASS.Comment: Accepted for Publication (MNRAS