Rare-Event Sampling: Occupation-Based Performance Measures for Parallel Tempering and Infinite Swapping Monte Carlo Methods

In the present paper we identify a rigorous property of a number of tempering-based Monte Carlo sampling methods, including parallel tempering as well as partial and infinite swapping. Based on this property we develop a variety of performance measures for such rare-event sampling methods that are broadly applicable, informative, and straightforward to implement. We illustrate the use of these performance measures with a series of applications involving the equilibrium properties of simple Lennard-Jones clusters, applications for which the performance levels of partial and infinite swapping approaches are found to be higher than those of conventional parallel tempering.Comment: 18 figure

An Infinite Swapping Approach to the Rare-Event Sampling Problem

We describe a new approach to the rare-event Monte Carlo sampling problem. This technique utilizes a symmetrization strategy to create probability distributions that are more highly connected and thus more easily sampled than their original, potentially sparse counterparts. After discussing the formal outline of the approach and devising techniques for its practical implementation, we illustrate the utility of the technique with a series of numerical applications to Lennard-Jones clusters of varying complexity and rare-event character.Comment: 24 pages, 16 figure

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

Discretization Dependence of Criticality in Model Fluids: a Hard-core Electrolyte

Grand canonical simulations at various levels, $\zeta=5$-20, of fine- lattice discretization are reported for the near-critical 1:1 hard-core electrolyte or RPM. With the aid of finite-size scaling analyses it is shown convincingly that, contrary to recent suggestions, the universal critical behavior is independent of $\zeta$ (\grtsim 4); thus the continuum $(\zeta\to\infty)$ RPM exhibits Ising-type (as against classical, SAW, XY, etc.) criticality. A general consideration of lattice discretization provides effective extrapolation of the {\em intrinsically} erratic $\zeta$-dependence, yielding (\Tc^ {\ast},\rhoc^{\ast})\simeq (0.0493_{3},0.075) for the $\zeta=\infty$ RPM.Comment: 4 pages including 4 figure

Nondielectric long-range solvation of polar liquids in cubic symmetry

Long-range solvation properties of strongly coupled dipolar systems simulated using the Ewald and reaction field methods are assessed by using electric fluctuation formulas for a dielectric medium. Some components of the fluctuating electric multipole moments are suppressed, whereas other components are favored as the boundary of the simulation box is approached. An analysis of electrostatic interactions in a periodic cubic system suggests that these structural effects are due to the periodicity embedded in the Ewald method. Furthermore, the results obtained using the reaction field method are very similar to those obtained using the Ewald method, an effect which we attribute to the use of toroidal boundary conditions in the former case. Thus, the long-range solvation properties of polar liquids simulated using either of the two methods are nondielectric in their character. (C) 2009 American Institute of Physics. [doi:10.1063/1.3250941

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

A Multiscale Approach to Determination of Thermal Properties and Changes in Free Energy: Application to Reconstruction of Dislocations in Silicon

We introduce an approach to exploit the existence of multiple levels of description of a physical system to radically accelerate the determination of thermodynamic quantities. We first give a proof of principle of the method using two empirical interatomic potential functions. We then apply the technique to feed information from an interatomic potential into otherwise inaccessible quantum mechanical tight-binding calculations of the reconstruction of partial dislocations in silicon at finite temperature. With this approach, comprehensive ab initio studies at finite temperature will now be possible.Comment: 5 pages, 3 figure

Criticality in confined ionic fluids

A theory of a confined two dimensional electrolyte is presented. The positive and negative ions, interacting by a $1/r$ potential, are constrained to move on an interface separating two solvents with dielectric constants $\epsilon_1$ and $\epsilon_2$. It is shown that the Debye-H\"uckel type of theory predicts that the this 2d Coulomb fluid should undergo a phase separation into a coexisting liquid (high density) and gas (low density) phases. We argue, however, that the formation of polymer-like chains of alternating positive and negative ions can prevent this phase transition from taking place.Comment: RevTex, no figures, in press Phys. Rev.

Sine-Gordon mean field theory of a Coulomb Gas

Sine-Gordon field theory is used to investigate the phase diagram of a neutral Coulomb gas. A variational mean field free energy is constructed and the corresponding phase diagrams in two (2d) and three dimensions (3d) are obtained. When analyzed in terms of chemical potential, the Sine-Gordon theory predicts the phase diagram topologically identical with the Monte Carlo simulations and a recently developed Debye-H\"uckel-Bjerrum (DHBj) theory. In 2d we find that the infinite order Kosterlitz-Thouless line terminates in a tricritical point, after which the metal-insulator transition becomes first order. However, when the transformation from chemical potential to the density is made the whole of the insulating phase is mapped onto zero density.Comment: 5 pages, Revtex with twocolumn style, 2 Postscript figures. Submitted to PR