"Exact" Algorithm for Random-Bond Ising Models in 2D

We present an efficient algorithm for calculating the properties of Ising models in two dimensions, directly in the spin basis, without the need for mapping to fermion or dimer models. The algorithm gives numerically exact results for the partition function and correlation functions at a single temperature on any planar network of N Ising spins in O(N^{3/2}) time or less. The method can handle continuous or discrete bond disorder and is especially efficient in the case of bond or site dilution, where it executes in O(L^2 ln L) time near the percolation threshold. We demonstrate its feasibility on the ferromagnetic Ising model and the +/- J random-bond Ising model (RBIM) and discuss the regime of applicability in cases of full frustration such as the Ising antiferromagnet on a triangular lattice.Comment: 4.2 pages, 5 figures, accepted for publication in Phys. Rev. Let

Noise Predictions for STM in Systems with Local Electron Nematic Order

We propose that thermal noise in local stripe orientation should be readily detectable via STM on systems in which local stripe orientations are strongly affected by quenched disorder. Stripes, a unidirectional, nanoscale modulation of electronic charge, are strongly affected by quenched disorder in two-dimensional and quasi-two-dimensional systems. While stripe orientations tend to lock to major lattice directions, dopant disorder locally breaks rotational symmetry. In a host crystal with otherwise $C_4$ rotational symmetry, stripe orientations in the presence of quenched disorder map to the random field Ising model. While the low temperature state of such a system is generally a stripe glass in two dimensional or strongly layered systems, as the temperature is raised, stripe orientational fluctuations become more prevalent. We propose that these thermally excited fluctuations should be readily detectable in scanning tunneling spectroscopy as {\em telegraph noise} in the high voltage part of the local $I(V)$ curves. We predict the spatial, temporal, and thermal evolution of such noise, including the circumstances under which such noise is most likely to be observed. In addition, we propose an in-situ test, amenable to any local scanning probe, for assessing whether such noise is due to correlated fluctuations rather than independent switchers.Comment: 8 pages, 8 figure

Short-Range Correlations and Cooling of Ultracold Fermions in the Honeycomb Lattice

We use determinantal quantum Monte Carlo simulations and numerical linked-cluster expansions to study thermodynamic properties and short-range spin correlations of fermions in the honeycomb lattice. We find that, at half filling and finite temperatures, nearest-neighbor spin correlations can be stronger in this lattice than in the square lattice, even in regimes where the ground state in the former is a semimetal or a spin liquid. The honeycomb lattice also exhibits a more pronounced anomalous region in the double occupancy that leads to stronger adiabatic cooling than in the square lattice. We discuss the implications of these findings for optical lattice experiments.Comment: 5 pages, 4 figure

Pairing Correlations in the Two-Dimensional Hubbard Model

We present the results of a quantum Monte Carlo study of the extended $s$ and the $d_{x^2-y^2}$ pairing correlation functions for the two-dimensional Hubbard model, computed with the constrained-path method. For small lattice sizes and weak interactions, we find that the $d_{x^2-y^2}$ pairing correlations are stronger than the extended $s$ pairing correlations and are positive when the pair separation exceeds several lattice constants. As the system size or the interaction strength increases, the magnitude of the long-range part of both correlation functions vanishes.Comment: 4 pages, RevTex, 4 figures included; submitted to Phys. Rev. Let

Evolution of pairing from weak to strong coupling on a honeycomb lattice

We study the evolution of the pairing from weak to strong coupling on a honeycomb lattice by Quantum Monte Carlo. We show numerical evidence of the BCS-BEC crossover as the coupling strength increases on a honeycomb lattice with small fermi surface by measuring a wide range of observables: double occupancy, spin susceptibility, local pair correlation, and kinetic energy. Although at low energy, the model sustains Dirac fermions, we do not find significant qualitative difference in the BCS-BEC crossover as compared to those with an extended Fermi surface, except at weak coupling, BCS regime.Comment: 5 page

A Time-Accurate Upwind Unstructured Finite Volume Method for Compressible Flow with Cure of Pathological Behaviors

A time-accurate, upwind, finite volume method for computing compressible flows on unstructured grids is presented. The method is second order accurate in space and time and yields high resolution in the presence of discontinuities. For efficiency, the Roe approximate Riemann solver with an entropy correction is employed. In the basic Euler/Navier-Stokes scheme, many concepts of high order upwind schemes are adopted: the surface flux integrals are carefully treated, a Cauchy-Kowalewski time-stepping scheme is used in the time-marching stage, and a multidimensional limiter is applied in the reconstruction stage. However even with these up-to-date improvements, the basic upwind scheme is still plagued by the so-called "pathological behaviors," e.g., the carbuncle phenomenon, the expansion shock, etc. A solution to these limitations is presented which uses a very simple dissipation model while still preserving second order accuracy. This scheme is referred to as the enhanced time-accurate upwind (ETAU) scheme in this paper. The unstructured grid capability renders flexibility for use in complex geometry; and the present ETAU Euler/Navier-Stokes scheme is capable of handling a broad spectrum of flow regimes from high supersonic to subsonic at very low Mach number, appropriate for both CFD (computational fluid dynamics) and CAA (computational aeroacoustics). Numerous examples are included to demonstrate the robustness of the methods

Vlasov Description Of Dense Quark Matter

We discuss properties of quark matter at finite baryon densities and zero temperature in a Vlasov approach. We use a screened interquark Richardson's potential consistent with the indications of Lattice QCD calculations. We analyze the choices of the quark masses and the parameters entering the potential which reproduce the binding energy (B.E.) of infinite nuclear matter. There is a transition from nuclear to quark matter at densities 5 times above normal nuclear matter density. The transition could be revealed from the determination of the position of the shifted meson masses in dense baryonic matter. A scaling form of the meson masses in dense matter is given.Comment: 15 pages 4 figure