A Generalization of Metropolis and Heat-Bath Sampling for Monte Carlo Simulations

For a wide class of applications of the Monte Carlo method, we describe a general sampling methodology that is guaranteed to converge to a specified equilibrium distribution function. The method is distinct from that of Metropolis in that it is sometimes possible to arrange for unconditional acceptance of trial moves. It involves sampling states in a local region of phase space with probability equal to, in the first approximation, the square root of the desired global probability density function. The validity of this choice is derived from the Chapman-Kolmogorov equation, and the utility of the method is illustrated by a prototypical numerical experiment.Comment: RevTeX, 7 pages, 2 table

Power sums of Coxeter exponents

Consider an irreducible finite Coxeter system. We show that for any nonnegative integer n the sum of the nth powers of the Coxeter exponents can be written uniformly as a polynomial in four parameters: h (the Coxeter number), r (the rank), and two further parameters.Comment: 14 page

Bayesian analysis of the radial velocities of HD 11506 reveals another planetary companion

We aim to demonstrate the efficiency of a Bayesian approach in analysing radial velocity data by reanalysing a set of radial velocity measurements. We present Bayesian analysis of a recently published set of radial velocity measurements known to contain the signal of one extrasolar planetary candidate, namely, HD 11506. The analysis is conducted using the Markov chain Monte Carlo method and the resulting distributions of orbital parameters are tested by performing direct integration of randomly selected samples with the Bulirsch-Stoer method. The magnitude of the stellar radial velocity variability, known as jitter, is treated as a free parameter with no assumptions about its magnitude. We show that the orbital parameters of the planet known to be present in the data correspond to a different solution when the jitter is allowed to be a free parameter. We also show evidence of an additional candidate, a 0.8 MJup planet with period of about 0.5 yr in orbit around HD 11506. This second planet is inferred to be present with a high level of confidence.Comment: 4 pages, 5 figures, to appear in A&

Wang-Landau sampling for quantum systems: algorithms to overcome tunneling problems and calculate the free energy

We present a generalization of the classical Wang-Landau algorithm [Phys. Rev. Lett. 86, 2050 (2001)] to quantum systems. The algorithm proceeds by stochastically evaluating the coefficients of a high temperature series expansion or a finite temperature perturbation expansion to arbitrary order. Similar to their classical counterpart, the algorithms are efficient at thermal and quantum phase transitions, greatly reducing the tunneling problem at first order phase transitions, and allow the direct calculation of the free energy and entropy.Comment: Added a plot showing the efficiency at first order phase transition

Configurational entropy of Wigner crystals

We present a theoretical study of classical Wigner crystals in two- and three-dimensional isotropic parabolic traps aiming at understanding and quantifying the configurational uncertainty due to the presence of multiple stable configurations. Strongly interacting systems of classical charged particles confined in traps are known to form regular structures. The number of distinct arrangements grows very rapidly with the number of particles, many of these arrangements have quite low occurrence probabilities and often the lowest-energy structure is not the most probable one. We perform numerical simulations on systems containing up to 100 particles interacting through Coulomb and Yukawa forces, and show that the total number of metastable configurations is not a well defined and representative quantity. Instead, we propose to rely on the configurational entropy as a robust and objective measure of uncertainty. The configurational entropy can be understood as the logarithm of the effective number of states; it is insensitive to the presence of overlooked low-probability states and can be reliably determined even within a limited time of a simulation or an experiment.Comment: 12 pages, 8 figures. This is an author-created, un-copyedited version of an article accepted for publication in J. Phys.: Condens. Matter. IOP Publishing Ltd is not responsible for any errors or omissions in this version of the manuscript or any version derived from it. The definitive publisher-authenticated version is available online at 10.1088/0953-8984/23/7/075302.

Monte Carlo approach of the islanding of polycrystalline thin films

We computed by a Monte Carlo method derived from the Solid on Solid model, the evolution of a polycrystalline thin film deposited on a substrate during thermal treatment. Two types of substrates have been studied: a single crystalline substrate with no defects and a single crystalline substrate with defects. We obtain islands which are either flat (i.e. with a height which does not overcome a given value) or grow in height like narrow towers. A good agreement was found regarding the morphology of numerical nanoislands at equilibrium, deduced from our model, and experimental nanoislands resulting from the fragmentation of YSZ thin films after thermal treatment.Comment: 20 pages, 7 figure

Constructing multiple unique input/output sequences using metaheuristic optimisation techniques

Multiple unique input/output sequences (UIOs) are often used to generate robust and compact test sequences in finite state machine (FSM) based testing. However, computing UIOs is NP-hard. Metaheuristic optimisation techniques (MOTs) such as genetic algorithms (GAs) and simulated annealing (SA) are effective in providing good solutions for some NP-hard problems. In the paper, the authors investigate the construction of UIOs by using MOTs. They define a fitness function to guide the search for potential UIOs and use sharing techniques to encourage MOTs to locate UIOs that are calculated as local optima in a search domain. They also compare the performance of GA and SA for UIO construction. Experimental results suggest that, after using a sharing technique, both GA and SA can find a majority of UIOs from the models under test

Low-energy quantum dynamics of atoms at defects. Interstitial oxygen in silicon

The problem of the low-energy highly-anharmonic quantum dynamics of isolated impurities in solids is addressed by using path-integral Monte Carlo simulations. Interstitial oxygen in silicon is studied as a prototypical example showing such a behavior. The assignment of a "geometry" to the defect is discussed. Depending on the potential (or on the impurity mass), there is a "classical" regime, where the maximum probability-density for the oxygen nucleus is at the potential minimum. There is another regime, associated to highly anharmonic potentials, where this is not the case. Both regimes are separated by a sharp transition. Also, the decoupling of the many-nuclei problem into a one-body Hamiltonian to describe the low-energy dynamics is studied. The adiabatic potential obtained from the relaxation of all the other degrees of freedom at each value of the coordinate associated to the low-energy motion, gives the best approximation to the full many-nuclei problem.Comment: RevTeX, 6 pages plus 4 figures (all the figures were not accesible before

Noisy Monte Carlo revisited

We present an exact Monte Carlo algorithm designed to sample theories where the energy is a sum of many couplings of decreasing strength. Our algorithm, simplified from that of L. Lin et al. hep-lat/9905033, avoids the computation of almost all non-leading terms. We illustrate its use by simulating SU(2) lattice gauge theory with a 5-loop action, and discuss further applications to full QCD.Comment: latex, 8 page

Projected single-spin flip dynamics in the Ising Model

We study transition matrices for projected dynamics in the energy-magnetization space, magnetization space and energy space. Several single spin flip dynamics are considered such as the Glauber and Metropolis canonical ensemble dynamics and the Metropolis dynamics for three multicanonical ensembles: the flat energy-magnetization histogram, the flat energy histogram and the flat magnetization histogram. From the numerical diagonalization of the matrices for the projected dynamics we obtain the sub-dominant eigenvalue and the largest relaxation times for systems of varying size. Although, the projected dynamics is an approximation to the full state space dynamics comparison with some available results, obtained by other authors, shows that projection in the magnetization space is a reasonably accurate method to study the scaling of relaxation times with system size. The transition matrices for arbitrary single-spin flip dynamics are obtained from a single Monte-Carlo estimate of the infinite temperature transition-matrix, for each system size, which makes the method an efficient tool to evaluate the relative performance of any arbitrary local spin-flip dynamics. We also present new results for appropriately defined average tunnelling times of magnetization and compute their finite-size scaling exponents that we compare with results of energy tunnelling exponents available for the flat energy histogram multicanonical ensemble.Comment: 23 pages and 6 figure