A Worm Algorithm for Two-Dimensional Spin Glasses

A worm algorithm is proposed for the two-dimensional spin glasses. The method is based on a low-temperature expansion of the partition function. The low-temperature configurations of the spin glass on square lattice can be viewed as strings connecting pairs of frustrated plaquettes. The worm algorithm directly manipulates these strings. It is shown that the worm algorithm is as efficient as any other types of cluster or replica-exchange algorithms. The worm algorithm is even more efficient if free boundary conditions are used. We obtain accurate low-temperature specific heat data consistent with a form c = T^{-2} exp(-2J/(k_BT)), where T is temperature and J is coupling constant, for the +/-J two-dimensional spin glass.Comment: 4 pages, 3 figure

A fast algorithm for random sequential adsorption of discs

An efficient algorithm for random sequential adsorption of hard discs in two dimensions is implemented. A precise value for the coverage is obtained: theta(infty) = 0.547069. The asymptotic law theta(t) = theta(infty) - ct^{-1/2} is verified to a high accuracy. Pair correlation function is analyzed.Comment: 7 pages + 4 figures, Plain TeX 3.14

Carbon Nanotube Thermal Transport: Ballistic to Diffusive

We propose to use l_0/(l_0+L) for the energy transmission covering both ballistic and diffusive regimes, where l_0 is mean free path and L is system length. This formula is applied to heat conduction in carbon nanotubes (CNTs). Calculations of thermal conduction show: (1) Thermal conductance at room temperature is proportional to the diameter of CNTs for single-walled CNTs (SWCNTs) and to the square of diameter for multi-walled CNTs (MWCNTs). (2) Interfaces play an important role in thermal conduction in CNTs due to the symmetry of CNTs vibrational modes. (3) When the phonon mean free path is comparable with the length L of CNTs in ballistic-diffusive regime, thermal conductivity \kappa goes as L^{\alpha} . The effective exponent \alpha is numerically found to decrease with increasing temperature and is insensitive to the diameter of SWCNTs for Umklapp scattering process. For short SWCNTs (<0.1 \mu m) we find \alpha \approx 0.8 at room temperature. These results are consistent with recent experimental findings.Comment: 4 pages, two figure

Transition Matrix Monte Carlo Method

We analyze a new Monte Carlo method which uses transition matrix in the space of energy. This method gives an efficient reweighting technique. The associated artificial dynamics is a constrained random walk in energy, producing the result that correlation time is proportional to the specific heat.Comment: LaTeX, 8 pages, 1 figur

Plancherel-Rotach Asymptotics of Second-Order Difference Equations with Linear Coefficients

In this paper, we provide a complete Plancherel-Rotach asymptotic analysis of polynomials that satisfy a second-order difference equation with linear coefficients. According to the signs of the parameters, we classify the difference equations into six cases and derive explicit asymptotic formulas of the polynomials in the outer and oscillatory regions, respectively. It is remarkable that the zero distributions of the polynomials may locate on the imaginary line or even on a sideways Y-shape curve in some cases