Classical dimers on the triangular lattice

We study the classical hard-core dimer model on the triangular lattice. Following Kasteleyn's fundamental theorem on planar graphs, this problem is soluble by Pfaffians. This model is particularly interesting for, unlike the dimer problems on the bipartite square and hexagonal lattices, its correlations are short ranged with a correlation length of less than one lattice constant. We compute the dimer-dimer and monomer-monomer correlators, and find that the model is deconfining: the monomer-monomer correlator falls off exponentially to a constant value sin(pi/12)/sqrt(3) = .1494..., only slightly below the nearest-neighbor value of 1/6. We also consider the anisotropic triangular lattice model in which the square lattice is perturbed by diagonal bonds of one orientation and small fugacity. We show that the model becomes non-critical immediately and that this perturbation is equivalent to adding a mass term to each of two Majorana fermions that are present in the long wavelength limit of the square-lattice problem.Comment: 15 pages, 5 figures. v2: includes analytic value of monomer-monomer correlator, changes titl

Continuous Percolation Phase Transitions of Two-dimensional Lattice Networks under a Generalized Achlioptas Process

The percolation phase transitions of two-dimensional lattice networks under a generalized Achlioptas process (GAP) are investigated. During the GAP, two edges are chosen randomly from the lattice and the edge with minimum product of the two connecting cluster sizes is taken as the next occupied bond with a probability $p$. At $p=0.5$, the GAP becomes the random growth model and leads to the minority product rule at $p=1$. Using the finite-size scaling analysis, we find that the percolation phase transitions of these systems with $0.5 \le p \le 1$ are always continuous and their critical exponents depend on $p$. Therefore, the universality class of the critical phenomena in two-dimensional lattice networks under the GAP is related to the probability parameter $p$ in addition.Comment: 7 pages, 14 figures, accepted for publication in Eur. Phys. J.

The Roton Fermi Liquid

We introduce and analyze a novel metallic phase of two-dimensional (2d) electrons, the Roton Fermi Liquid (RFL), which, in contrast to the Landau Fermi liquid, supports both gapless fermionic and bosonic quasiparticle excitations. The RFL is accessed using a re-formulation of 2d electrons consisting of fermionic quasiparticles and $hc/2e$ vortices interacting with a mutual long-ranged statistical interaction. In the presence of a strong vortex-antivortex (i.e. roton) hopping term, the RFL phase emerges as an exotic yet eminently tractable new quantum ground state. The RFL phase exhibits a ``Bose surface'' of gapless roton excitations describing transverse current fluctuations, has off-diagonal quasi-long-ranged order (ODQLRO) at zero temperature (T=0), but is not superconducting, having zero superfluid density and no Meissner effect. The electrical resistance {\it vanishes} as $T \to 0$ with a power of temperature (and frequency), $R(T) \sim T^\gamma$ (with $\gamma >1$), independent of the impurity concentration. The RFL phase also has a full Fermi surface of quasiparticle excitations just as in a Landau Fermi liquid. Electrons can, however, scatter anomalously from rotonic "current fluctuations'' and "superconducting fluctuations'', leading to "hot" and "cold" spots. Fermionic quasiparticles dominate the Hall electrical transport. We also discuss instabilities of the RFL to a conventional Fermi liquid and a superconductor. Precisely {\it at} the instability into the Fermi liquid state, the exponent $\gamma =1$, so that $R(T) \sim T$. Upon entering the superconducting state the anomalous quasiparticle scattering is strongly suppressed. We discuss how the RFL phenomenology might apply to the cuprates.Comment: 43 page

POTENT Reconstruction from Mark III Velocities

We present an improved POTENT method for reconstructing the velocity and mass density fields from radial peculiar velocities, test it with mock catalogs, and apply it to the Mark III Catalog. Method improvments: (a) inhomogeneous Malmquist bias is reduced by grouping and corrected in forward or inverse analyses of inferred distances, (b) the smoothing into a radial velocity field is optimized to reduce window and sampling biases, (c) the density is derived from the velocity using an improved nonlinear approximation, and (d) the computational errors are made negligible. The method is tested and optimized using mock catalogs based on an N-body simulation that mimics our cosmological neighborhood, and the remaining errors are evaluated quantitatively. The Mark III catalog, with ~3300 grouped galaxies, allows a reliable reconstruction with fixed Gaussian smoothing of 10-12 Mpc/h out to ~60 Mpc/h. We present maps of the 3D velocity and mass-density fields and the corresponding errors. The typical systematic and random errors in the density fluctuations inside 40 Mpc/h are \pm 0.13 and \pm 0.18. The recovered mass distribution resembles in its gross features the galaxy distribution in redshift surveys and the mass distribution in a similar POTENT analysis of a complementary velocity catalog (SFI), including the Great Attractor, Perseus-Pisces, and the void in between. The reconstruction inside ~40 Mpc/h is not affected much by a revised calibration of the distance indicators (VM2, tailored to match the velocities from the IRAS 1.2Jy redshift survey). The bulk velocity within the sphere of radius 50 Mpc/h about the Local Group is V_50=370 \pm 110 km/s (including systematic errors), and is shown to be mostly generated by external mass fluctuations. With the VM2 calibration, V_50 is reduced to 305 \pm 110 km/s.Comment: 60 pages, LaTeX, 3 tables and 27 figures incorporated (may print the most crucial figures only, by commenting out one line in the LaTex source

Ultraviolet Broad Absorption Features and the Spectral Energy Distribution of the QSO PG 1351+64

We present a moderate-resolution (~20 km/s) spectrum of the mini broad-absorption-line QSO PG1351+64 between 915-1180 A, obtained with the Far Ultraviolet Spectroscopic Explorer (FUSE). Additional spectra at longer wavelengths were also obtained with the HST and ground-based telescopes. Broad absorption is present on the blue wings of CIII 977, Ly-beta, OVI 1032,1038, Ly-alpha, NV 1238,1242, SiIV 1393,1402, and CIV 1548,1450. The absorption profile can be fitted with five components at velocities of ~ -780, -1049, -1629, -1833, and -3054 km/s with respect to the emission-line redshift of z = 0.088. All the absorption components cover a large fraction of the continuum source as well as the broad-line region. The OVI emission feature is very weak, and the OVI/Lyalpha flux ratio is 0.08, one of the lowest among low-redshift active galaxies and QSOs. The UV continuum shows a significant change in slope near 1050 A in the restframe. The steeper continuum shortward of the Lyman limit extrapolates well to the observed weak X-ray flux level. The absorbers' properties are similar to those of high-redshift broad absorption-line QSOs. The derived total column density of the UV absorbers is on the order of 10^21 cm^-2, unlikely to produce significant opacity above 1 keV in the X-ray. Unless there is a separate, high-ionization X-ray absorber, the QSO's weak X-ray flux may be intrinsic. The ionization level of the absorbing components is comparable to that anticipated in the broad-line region, therefore the absorbers may be related to broad-line clouds along the line of sight.Comment: 23 pages, Latex, 5 figure

Scaling in the Lattice Gas Model

A good quality scaling of the cluster size distributions is obtained for the Lattice Gas Model using the Fisher's ansatz for the scaling function. This scaling identifies a pseudo-critical line in the phase diagram of the model that spans the whole (subcritical to supercritical) density range. The independent cluster hypothesis of the Fisher approach is shown to describe correctly the thermodynamics of the lattice only far away from the critical point.Comment: 4 pages, 3 figure

Finite Size Analysis of Luttinger Liquids with a source of 2k_f Scattering

Numerical analysis of the spectrum of large finite size Luttinger liquids (g<1) in the presence of a single source of 2k_f scattering has been made possible thanks to an effective integration of high degrees of freedom. Presence of irrelevant operators and their manifestation in transport are issues treated independently. We confirm the existence of two irrelevant operators: particle hopping and charge oscillations, with regions of dominance separated by g=1/2. Temperature dependence of conductance is shown to be dominated by hopping alone. Frequency dependence is affected by both irrelevant operators.Comment: 4 pages, LaTex (RevTex), 3 PostScript figures appende

Doping induced metal-insulator transition in two-dimensional Hubbard, t−Ut-U, and extended Hubbard, t−U−Wt-U-W, models

We show numerically that the nature of the doping induced metal-insulator transition in the two-dimensional Hubbard model is radically altered by the inclusion of a term, $W$, which depends upon a square of a single-particle nearest-neighbor hopping. This result is reached by computing the localization length, $\xi_l$, in the insulating state. At finite values of $W$ we find results consistent with $\xi_l \sim | \mu - \mu_c|^{- 1/2}$ where $\mu_c$ is the critical chemical potential. In contrast, $\xi_l \sim | \mu - \mu_c|^{-1/4}$ for the Hubbard model. At finite values of $W$, the presented numerical results imply that doping the antiferromagnetic Mott insulator leads to a $d_{x^2 - y ^2}$ superconductor.Comment: 19 pages (latex) including 7 figures in encapsulated postscript format. Submitted for publication in Phys. Rev.

On the finite-size behavior of systems with asymptotically large critical shift

Exact results of the finite-size behavior of the susceptibility in three-dimensional mean spherical model films under Dirichlet-Dirichlet, Dirichlet-Neumann and Neumann-Neumann boundary conditions are presented. The corresponding scaling functions are explicitly derived and their asymptotics close to, above and below the bulk critical temperature $T_c$ are obtained. The results can be incorporated in the framework of the finite-size scaling theory where the exponent $\lambda$ characterizing the shift of the finite-size critical temperature with respect to $T_c$ is smaller than $1/\nu$, with $\nu$ being the critical exponent of the bulk correlation length.Comment: 24 pages, late