Multicanonical Recursions

The problem of calculating multicanonical parameters recursively is discussed. I describe in detail a computational implementation which has worked reasonably well in practice.Comment: 23 pages, latex, 4 postscript figures included (uuencoded Z-compressed .tar file created by uufiles), figure file corrected

On the Wang-Landau Method for Off-Lattice Simulations in the "Uniform" Ensemble

We present a rigorous derivation for off-lattice implementations of the so-called "random-walk" algorithm recently introduced by Wang and Landau [PRL 86, 2050 (2001)]. Originally developed for discrete systems, the algorithm samples configurations according to their inverse density of states using Monte-Carlo moves; the estimate for the density of states is refined at each simulation step and is ultimately used to calculate thermodynamic properties. We present an implementation for atomic systems based on a rigorous separation of kinetic and configurational contributions to the density of states. By constructing a "uniform" ensemble for configurational degrees of freedom--in which all potential energies, volumes, and numbers of particles are equally probable--we establish a framework for the correct implementation of simulation acceptance criteria and calculation of thermodynamic averages in the continuum case. To demonstrate the generality of our approach, we perform sample calculations for the Lennard-Jones fluid using two implementation variants and in both cases find good agreement with established literature values for the vapor-liquid coexistence locus.Comment: 21 pages, 4 figure

Monte Carlo simulation and global optimization without parameters

We propose a new ensemble for Monte Carlo simulations, in which each state is assigned a statistical weight $1/k$, where $k$ is the number of states with smaller or equal energy. This ensemble has robust ergodicity properties and gives significant weight to the ground state, making it effective for hard optimization problems. It can be used to find free energies at all temperatures and picks up aspects of critical behaviour (if present) without any parameter tuning. We test it on the travelling salesperson problem, the Edwards-Anderson spin glass and the triangular antiferromagnet.Comment: 10 pages with 3 Postscript figures, to appear in Phys. Rev. Lett

Grundstate Properties of the 3D Ising Spin Glass

We study zero--temperature properties of the 3d Edwards--Anderson Ising spin glass on finite lattices up to size $12^3$. Using multicanonical sampling we generate large numbers of groundstate configurations in thermal equilibrium. Finite size scaling with a zero--temperature scaling exponent $y = 0.74 \pm 0.12$ describes the data well. Alternatively, a descriptions in terms of Parisi mean field behaviour is still possible. The two scenarios give significantly different predictions on lattices of size $\ge 12^3$.Comment: LATEX 9pages,figures upon request ,SCRI-9

Long spin relaxation times in wafer scale epitaxial graphene on SiC(0001)

We developed an easy, upscalable process to prepare lateral spin-valve devices on epitaxially grown monolayer graphene on SiC(0001) and perform nonlocal spin transport measurements. We observe the longest spin relaxation times tau_S in monolayer graphene, while the spin diffusion coefficient D_S is strongly reduced compared to typical results on exfoliated graphene. The increase of tau_S is probably related to the changed substrate, while the cause for the small value of D_S remains an open question.Comment: 16 pages, 3 figures, 1 tabl

Parallelization of Markov chain generation and its application to the multicanonical method

We develop a simple algorithm to parallelize generation processes of Markov chains. In this algorithm, multiple Markov chains are generated in parallel and jointed together to make a longer Markov chain. The joints between the constituent Markov chains are processed using the detailed balance. We apply the parallelization algorithm to multicanonical calculations of the two-dimensional Ising model and demonstrate accurate estimation of multicanonical weights.Comment: 15 pages, 5 figures, uses elsart.cl

Stacking Entropy of Hard Sphere Crystals

Classical hard spheres crystallize at equilibrium at high enough density. Crystals made up of stackings of 2-dimensional hexagonal close-packed layers (e.g. fcc, hcp, etc.) differ in entropy by only about $10^{-3}k_B$ per sphere (all configurations are degenerate in energy). To readily resolve and study these small entropy differences, we have implemented two different multicanonical Monte Carlo algorithms that allow direct equilibration between crystals with different stacking sequences. Recent work had demonstrated that the fcc stacking has higher entropy than the hcp stacking. We have studied other stackings to demonstrate that the fcc stacking does indeed have the highest entropy of ALL possible stackings. The entropic interactions we could detect involve three, four and (although with less statistical certainty) five consecutive layers of spheres. These interlayer entropic interactions fall off in strength with increasing distance, as expected; this fall-off appears to be much slower near the melting density than at the maximum (close-packing) density. At maximum density the entropy difference between fcc and hcp stackings is $0.00115 +/- 0.00004 k_B$ per sphere, which is roughly 30% higher than the same quantity measured near the melting transition.Comment: 15 page

A Multicanonical Molecular Dynamics Study on a Simple Bead-Spring Model for Protein Folding

We have performed a multicanonical molecular dynamics simulation on a simple model protein.We have studied a model protein composed of charged, hydrophobic, and neutral spherical bead monomers.Since the hydrophobic interaction is considered to significantly affect protein folding, we particularly focus on the competition between effects of the Coulomb interaction and the hydrophobic interaction. We found that the transition which occurs upon decreasing the temperature is markedly affected by the change in both parameters and forms of the hydrophobic potential function, and the transition changes from first order to second order, when the Coulomb interaction becomes weaker.Comment: 7 pages, 6 postscript figures, To appear in J.Phys.Soc.Jpn. Vol.70 No.

A comparison of extremal optimization with flat-histogram dynamics for finding spin-glass ground states

We compare the performance of extremal optimization (EO), flat-histogram and equal-hit algorithms for finding spin-glass ground states. The first-passage-times to a ground state are computed. At optimal parameter of tau=1.15, EO outperforms other methods for small system sizes, but equal-hit algorithm is competitive to EO, particularly for large systems. Flat-histogram and equal-hit algorithms offer additional advantage that they can be used for equilibrium thermodynamic calculations. We also propose a method to turn EO into a useful algorithm for equilibrium calculations. Keywords: extremal optimization. flat-histogram algorithm, equal-hit algorithm, spin-glass model, ground state.Comment: 10 LaTeX pages, 2 figure