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

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

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.

Multiple Histogram Method for Quantum Monte Carlo

An extension to the multiple-histogram method (sometimes referred to as the Ferrenberg-Swendsen method) for use in quantum Monte Carlo simulations is presented. This method is shown to work well for the 2D repulsive Hubbard model, allowing measurements to be taken over a continuous region of parameters. The method also reduces the error bars over the range of parameter values due the overlapping of multiple histograms. A continuous sweep of parameters and reduced error bars allow one to make more difficult measurements, such as Maxwell constructions used to study phase separation. Possibilities also exist for this method to be used for other quantum systems.Comment: 4 pages, 5 figures, RevTeX, submitted to Phys. Rev. B Rapid Com

Criticality in polar fluids

A model of polar fluid is studied theoretically. The interaction potential, in addition to dipole-dipole term, possesses a dispersion contribution of the van der Waals-London form. It is found that when the dispersion force is comparable to dipole-dipole interaction, the fluid separates into coexisting liquid and gas phases. The calculated critical parameters are in excellent agreement with Monte Carlo simulations. When the strength of dispersion attraction is bellow critical, no phase separation is found.Comment: 5 pages, 2 figures, references modifie

Asymmetric Fluid Criticality II: Finite-Size Scaling for Simulations

The vapor-liquid critical behavior of intrinsically asymmetric fluids is studied in finite systems of linear dimensions, $L$, focusing on periodic boundary conditions, as appropriate for simulations. The recently propounded ``complete'' thermodynamic $(L\to\infty)$ scaling theory incorporating pressure mixing in the scaling fields as well as corrections to scaling ${[arXiv:cond-mat/0212145]}$, is extended to finite $L$, initially in a grand canonical representation. The theory allows for a Yang-Yang anomaly in which, when $L\to\infty$, the second temperature derivative, $(d^{2}\mu_{\sigma}/dT^{2})$, of the chemical potential along the phase boundary, $\mu_{\sigma}(T)$, diverges when T\to\Tc -. The finite-size behavior of various special {\em critical loci} in the temperature-density or $(T,\rho)$ plane, in particular, the $k$-inflection susceptibility loci and the $Q$-maximal loci -- derived from $Q_{L}(T,_{L}) \equiv ^{2}_{L}/< m^{4}>_{L}$ where $m \equiv \rho - _{L}$ -- is carefully elucidated and shown to be of value in estimating \Tc and \rhoc. Concrete illustrations are presented for the hard-core square-well fluid and for the restricted primitive model electrolyte including an estimate of the correlation exponent $\nu$ that confirms Ising-type character. The treatment is extended to the canonical representation where further complications appear.Comment: 23 pages in the two-column format (including 13 figures) This is Part II of the previous paper [arXiv:cond-mat/0212145

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

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

Multicanonical Multigrid Monte Carlo

To further improve the performance of Monte Carlo simulations of first-order phase transitions we propose to combine the multicanonical approach with multigrid techniques. We report tests of this proposition for the $d$-dimensional $\Phi^4$ field theory in two different situations. First, we study quantum tunneling for $d = 1$ in the continuum limit, and second, we investigate first-order phase transitions for $d = 2$ in the infinite volume limit. Compared with standard multicanonical simulations we obtain improvement factors of several resp. of about one order of magnitude.Comment: 12 pages LaTex, 1 PS figure appended. FU-Berlin preprint FUB-HEP 9/9