Optimized energy calculation in lattice systems with long-range interactions

We discuss an efficient approach to the calculation of the internal energy in numerical simulations of spin systems with long-range interactions. Although, since the introduction of the Luijten-Bl\"ote algorithm, Monte Carlo simulations of these systems no longer pose a fundamental problem, the energy calculation is still an O(N^2) problem for systems of size N. We show how this can be reduced to an O(N logN) problem, with a break-even point that is already reached for very small systems. This allows the study of a variety of, until now hardly accessible, physical aspects of these systems. In particular, we combine the optimized energy calculation with histogram interpolation methods to investigate the specific heat of the Ising model and the first-order regime of the three-state Potts model with long-range interactions.Comment: 10 pages, including 8 EPS figures. To appear in Phys. Rev. E. Also available as PDF file at http://www.cond-mat.physik.uni-mainz.de/~luijten/erikpubs.htm

Monte Carlo investigations of phase transitions: status and perspectives

Using the concept of finite-size scaling, Monte Carlo calculations of various models have become a very useful tool for the study of critical phenomena, with the system linear dimension as a variable. As an example, several recent studies of Ising models are discussed, as well as the extension to models of polymer mixtures and solutions. It is shown that using appropriate cluster algorithms, even the scaling functions describing the crossover from the Ising universality class to the mean-field behavior with increasing interaction range can be described. Additionally, the issue of finite-size scaling in Ising models above the marginal dimension (d*=4) is discussed.Comment: 23 pages, including 14 PostScript figures. Presented at StatPhys-Taiwan, August 9-16, 1999. Also available as PDF file at http://www.cond-mat.physik.uni-mainz.de/~luijten/erikpubs.htm

Stabilization of colloidal suspensions by means of highly-charged nanoparticles

We employ a novel Monte Carlo simulation scheme to elucidate the stabilization of neutral colloidal microspheres by means of highly-charged nanoparticles [V. Tohver et al., Proc. Natl. Acad. Sci. U.S.A. 98, 8950 (2001)]. In accordance with the experimental observations, we find that small nanoparticle concentrations induce an effective repulsion that prevents gelation caused by the intrinsic van der Waals attraction between colloids. Higher nanoparticle concentrations induce an attractive potential which is, however, qualitatively different from the regular depletion attraction. We also show how colloid-nanoparticle size asymmetry and nanoparticle charge can be used to manipulate the effective interactions.Comment: Accepted for publication in Physical Review Letters. See also S. Karanikas and A.A. Louis, cond-mat/0411279. Updated to synchronize with published versio

Monte Carlo cluster algorithm for fluid phase transitions in highly size-asymmetrical binary mixtures

Highly size-asymmetrical fluid mixtures arise in a variety of physical contexts, notably in suspensions of colloidal particles to which much smaller particles have been added in the form of polymers or nanoparticles. Conventional schemes for simulating models of such systems are hamstrung by the difficulty of relaxing the large species in the presence of the small one. Here we describe how the rejection-free geometrical cluster algorithm (GCA) of Liu and Luijten [Phys. Rev. Lett 92, 035504 (2004)] can be embedded within a restricted Gibbs ensemble to facilitate efficient and accurate studies of fluid phase behavior of highly size-asymmetrical mixtures. After providing a detailed description of the algorithm, we summarize the bespoke analysis techniques of Ashton et al. [J. Chem. Phys. 132, 074111 (2010)] that permit accurate estimates of coexisting densities and critical-point parameters. We apply our methods to study the liquid--vapor phase diagram of a particular mixture of Lennard-Jones particles having a 10:1 size ratio. As the reservoir volume fraction of small particles is increased in the range 0--5%, the critical temperature decreases by approximately 50%, while the critical density drops by some 30%. These trends imply that in our system, adding small particles decreases the net attraction between large particles, a situation that contrasts with hard-sphere mixtures where an attractive depletion force occurs.Comment: 11 pages, 10 figure

Colloidal stabilization via nanoparticle haloing

We present a detailed numerical study of effective interactions between micron-sized silica spheres, induced by highly charged zirconia nanoparticles. It is demonstrated that the effective interactions are consistent with a recently discovered mechanism for colloidal stabilization. In accordance with the experimental observations, small nanoparticle concentrations induce an effective repulsion that counteracts the intrinsic van der Waals attraction between the colloids and thus stabilizes the suspension. At higher nanoparticle concentrations an attractive potential is recovered, resulting in reentrant gelation. Monte Carlo simulations of this highly size-asymmetric mixture are made possible by means of a geometric cluster Monte Carlo algorithm. A comparison is made to results obtained from the Ornstein-Zernike equations with the hypernetted-chain closure

Crossover phenomena in spin models with medium-range interactions and self-avoiding walks with medium-range jumps

We study crossover phenomena in a model of self-avoiding walks with medium-range jumps, that corresponds to the limit $N\to 0$ of an $N$-vector spin system with medium-range interactions. In particular, we consider the critical crossover limit that interpolates between the Gaussian and the Wilson-Fisher fixed point. The corresponding crossover functions are computed using field-theoretical methods and an appropriate mean-field expansion. The critical crossover limit is accurately studied by numerical Monte Carlo simulations, which are much more efficient for walk models than for spin systems. Monte Carlo data are compared with the field-theoretical predictions concerning the critical crossover functions, finding a good agreement. We also verify the predictions for the scaling behavior of the leading nonuniversal corrections. We determine phenomenological parametrizations that are exact in the critical crossover limit, have the correct scaling behavior for the leading correction, and describe the nonuniversal lscrossover behavior of our data for any finite range.Comment: 43 pages, revte

A Monte Carlo study of the three-dimensional Coulomb frustrated Ising ferromagnet

We have investigated by Monte-Carlo simulation the phase diagram of a three-dimensional Ising model with nearest-neighbor ferromagnetic interactions and small, but long-range (Coulombic) antiferromagnetic interactions. We have developed an efficient cluster algorithm and used different lattice sizes and geometries, which allows us to obtain the main characteristics of the temperature-frustration phase diagram. Our finite-size scaling analysis confirms that the melting of the lamellar phases into the paramgnetic phase is driven first-order by the fluctuations. Transitions between ordered phases with different modulation patterns is observed in some regions of the diagram, in agreement with a recent mean-field analysis.Comment: 14 pages, 10 figures, submitted to Phys. Rev.

The importance of correcting for signal drift in diffusion MRI

Purpose To investigate previously unreported effects of signal drift as a result of temporal scanner instability on diffusion MRI data analysis and to propose a method to correct this signal drift. Methods We investigated the signal magnitude of non-diffusion-weighted EPI volumes in a series of diffusion-weighted imaging experiments to determine whether signal magnitude changes over time. Different scan protocols and scanners from multiple vendors were used to verify this on phantom data, and the effects on diffusion kurtosis tensor estimation in phantom and in vivo data were quantified. Scalar metrics (eigenvalues, fractional anisotropy, mean diffusivity, mean kurtosis) and directional information (first eigenvectors and tractography) were investigated. Results Signal drift, a global signal decrease with subsequently acquired images in the scan, was observed in phantom data on all three scanners, with varying magnitudes up to 5% in a 15-min scan. The signal drift has a noticeable effect on the estimation of diffusion parameters. All investigated quantitative parameters as well as tractography were affected by this artifactual signal decrease during the scan. Conclusion By interspersing the non-diffusion-weighted images throughout the session, the signal decrease can be estimated and compensated for before data analysis; minimizing the detrimental effects on subsequent MRI analyses. Magn Reson Med 77:285–299, 2017. © 2016 The Authors Magnetic Resonance in Medicine published by Wiley Periodicals, Inc. on behalf of International Society for Magnetic Resonance in Medicine

On the Symmetry of Universal Finite-Size Scaling Functions in Anisotropic Systems

In this work a symmetry of universal finite-size scaling functions under a certain anisotropic scale transformation is postulated. This transformation connects the properties of a finite two-dimensional system at criticality with generalized aspect ratio $\rho > 1$ to a system with $\rho < 1$. The symmetry is formulated within a finite-size scaling theory, and expressions for several universal amplitude ratios are derived. The predictions are confirmed within the exactly solvable weakly anisotropic two-dimensional Ising model and are checked within the two-dimensional dipolar in-plane Ising model using Monte Carlo simulations. This model shows a strongly anisotropic phase transition with different correlation length exponents $\nu_{||} \neq \nu_\perp$ parallel and perpendicular to the spin axis.Comment: RevTeX4, 4 pages, 3 figure

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