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

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.

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

The complementarity of astrometric and radial velocity exoplanet observations - Determining exoplanet mass with astrometric snapshots

We obtain full information on the orbital parameters by combining radial velocity and astrometric measurements by means of Bayesian inference. We sample the parameter probability densities of orbital model parameters with a Markov chain Monte Carlo (McMC) method in simulated observational scenarios to test the detectability of planets with orbital periods longer than the observational timelines. We show that, when fitting model parameters simultaneously to measurements from both sources, it is possible to extract much more information from the measurements than when using either source alone. We demonstrate this by studying the orbit of recently found extra-solar planet HD 154345 b.Comment: 6 pages, 9 figures. Accepted to A&

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

Evidence for 9 planets in the HD 10180 system

We re-analyse the HARPS radial velocities of HD 10180 and calculate the probabilities of models with differing numbers of periodic signals in the data. We test the significance of the seven signals, corresponding to seven exoplanets orbiting the star, in the Bayesian framework and perform comparisons of models with up to nine periodicities. We use posterior samplings and Bayesian model probabilities in our analyses together with suitable prior probability densities and prior model probabilities to extract all the significant signals from the data and to receive reliable uncertainties for the orbital parameters of the six, possibly seven, known exoplanets in the system. According to our results, there is evidence for up to nine planets orbiting HD 10180, which would make this this star a record holder in having more planets in its orbits than there are in the Solar system. We revise the uncertainties of the previously reported six planets in the system, verify the existence of the seventh signal, and announce the detection of two additional statistically significant signals in the data. If of planetary origin, these two additional signals would correspond to planets with minimum masses of 5.1$^{+3.1}_{-3.2}$ and 1.9$^{+1.6}_{-1.8}$ M$_{\oplus}$ on orbits with 67.55$^{+0.68}_{-0.88}$ and 9.655$^{+0.022}_{-0.072}$ days periods (denoted using the 99% credibility intervals), respectively.Comment: 12 pages, 7 figures, accepted for publication in the Astronomy and Astrophysic

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

Cluster emission and phase transition behaviours in nuclear disassembly

The features of the emissions of light particles (LP), charged particles (CP), intermediate mass fragments (IMF) and the largest fragment (MAX) are investigated for $^{129}Xe$ as functions of temperature and 'freeze-out' density in the frameworks of the isospin-dependent lattice gas model and the classical molecular dynamics model. Definite turning points for the slopes of average multiplicity of LP, CP and IMF, and of the mean mass of the largest fragment ($A_{max}$) are shown around a liquid-gas phase transition temperature and while the largest variances of the distributions of LP, CP, IMF and MAX appear there. It indicates that the cluster emission rate can be taken as a probe of nuclear liquid--gas phase transition. Furthermore, the largest fluctuation is simultaneously accompanied at the point of the phase transition as can be noted by investigating both the variances of their cluster multiplicity or mass distributions and the Campi scatter plots within the lattice gas model and the molecular dynamics model, which is consistent with the result of the traditional thermodynamical theory when a phase transition occurs.Comment: replace nucl-th/0103009 due to the technique problem to access old versio

Monte Carlo Study of the Separation of Energy Scales in Quantum Spin 1/2 Chains with Bond Disorder

One-dimensional Heisenberg spin 1/2 chains with random ferro- and antiferromagnetic bonds are realized in systems such as $Sr_3 CuPt_{1-x} Ir_x O_6$. We have investigated numerically the thermodynamic properties of a generic random bond model and of a realistic model of $Sr_3 CuPt_{1-x} Ir_x O_6$ by the quantum Monte Carlo loop algorithm. For the first time we demonstrate the separation into three different temperature regimes for the original Hamiltonian based on an exact treatment, especially we show that the intermediate temperature regime is well-defined and observable in both the specific heat and the magnetic susceptibility. The crossover between the regimes is indicated by peaks in the specific heat. The uniform magnetic susceptibility shows Curie-like behavior in the high-, intermediate- and low-temperature regime, with different values of the Curie constant in each regime. We show that these regimes are overlapping in the realistic model and give numerical data for the analysis of experimental tests.Comment: 7 pages, 5 eps-figures included, typeset using JPSJ.sty, accepted for publication in J. Phys. Soc. Jpn. 68, Vol. 3. (1999