Comment on ``Scaling Laws for a System with Long-Range Interactions within Tsallis Statistics''

In their recent Letter [Phys. Rev. Lett. 83, 4233 (1999)], Salazar and Toral (ST) study numerically a finite Ising chain with non-integrable interactions decaying like 1/r^(d+sigma) where -d <= sigma <= 0 (like ST, we discuss general dimensionality d). In particular, they explore a presumed connection between non-integrable interactions and Tsallis's non-extensive statistics. We point out that (i) non-integrable interactions provide no more motivation for Tsallis statistics than do integrable interactions, i.e., Gibbs statistics remain meaningful for the non-integrable case, and in fact provide a {\em complete and exact treatment}; and (ii) there are undesirable features of the method ST use to regulate the non-integrable interactions.Comment: Accepted for publication in Phys. Rev. Let

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

Quantum spin chains with site dissipation

We use Monte Carlo simulations to study chains of Ising- and XY-spins with dissipation coupling to the site variables. The phase diagram and critical exponents of the dissipative Ising chain in a transverse magnetic field have been computed previously, and here we consider a universal ratio of susceptibilities. We furthermore present the phase diagram and exponents of the dissipative XY-chain, which exhibits a second order phase transition. All our results compare well with the predictions from a dissipative $\phi^4$ field theory

Generalized Geometric Cluster Algorithm for Fluid Simulation

We present a detailed description of the generalized geometric cluster algorithm for the efficient simulation of continuum fluids. The connection with well-known cluster algorithms for lattice spin models is discussed, and an explicit full cluster decomposition is derived for a particle configuration in a fluid. We investigate a number of basic properties of the geometric cluster algorithm, including the dependence of the cluster-size distribution on density and temperature. Practical aspects of its implementation and possible extensions are discussed. The capabilities and efficiency of our approach are illustrated by means of two example studies.Comment: Accepted for publication in Phys. Rev. E. Follow-up to cond-mat/041274

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

Critical behavior of the long-range Ising chain from the largest-cluster probability distribution

Monte Carlo simulations of the 1D Ising model with ferromagnetic interactions decaying with distance $r$ as $1/r^{1+\sigma}$ are performed by applying the Swendsen-Wang cluster algorithm with cumulative probabilities. The critical behavior in the non-classical critical regime corresponding to $0.5 <\sigma < 1$ is derived from the finite-size scaling analysis of the largest cluster.Comment: 4 pages, 2 figures, in RevTeX, to appear in Phys. Rev. E (Feb 2001

Rejection-free Geometric Cluster Algorithm for Complex Fluids

We present a novel, generally applicable Monte Carlo algorithm for the simulation of fluid systems. Geometric transformations are used to identify clusters of particles in such a manner that every cluster move is accepted, irrespective of the nature of the pair interactions. The rejection-free and non-local nature of the algorithm make it particularly suitable for the efficient simulation of complex fluids with components of widely varying size, such as colloidal mixtures. Compared to conventional simulation algorithms, typical efficiency improvements amount to several orders of magnitude

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.

Thinner Regions of Intracranial Aneurysm Wall Correlate with Regions of Higher Wall Shear Stress: A 7T MRI Study

BACKGROUND AND PURPOSE: Both hemodynamics and aneurysm wall thickness are important parameters in aneurysm pathophysiology. Our aim was to develop a method for semi-quantitative wall thickness assessment on in vivo 7T MR images of intracranial aneurysms for studying the relation between apparent aneurysm wall thickness and wall shear stress. MATERIALS AND METHODS: Wall thickness was analyzed in 11 unruptured aneurysms in 9 patients who underwent 7T MR imaging with a TSE-based vessel wall sequence (0.8-mm isotropic resolution). A custom analysis program determined the in vivo aneurysm wall intensities, which were normalized to the signal of nearby brain tissue and were used as measures of apparent wall thickness. Spatial wall thickness variation was determined as the interquartile range in apparent wall thickness (the middle 50% of the apparent wall thickness range). Wall shear stress was determined by using phase-contrast MR imaging (0.5-mm isotropic resolution). We performed visual and statistical comparisons (Pearson correlation) to study the relation between wall thickness and wall shear stress. RESULTS: 3D colored apparent wall thickness maps of the aneurysms showed spatial apparent wall thickness variation, which ranged from 0.07 to 0.53, with a mean variation of 0.22 (a variation of 1.0 roughly means a wall thickness variation of 1 voxel [0.8 mm]). In all aneurysms, apparent wall thickness was inversely related to wall shear stress (mean correlation coefficient, −0.35; P < .05). CONCLUSIONS: A method was developed to measure the wall thickness semi-quantitatively, by using 7T MR imaging. An inverse correlation between wall shear stress and apparent wall thickness was determined. In future studies, this noninvasive method can be used to assess spatial wall thickness variation in relation to pathophysiologic processes such as aneurysm growth and rupture