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

Nonmonotonical crossover of the effective susceptibility exponent

We have numerically determined the behavior of the magnetic susceptibility upon approach of the critical point in two-dimensional spin systems with an interaction range that was varied over nearly two orders of magnitude. The full crossover from classical to Ising-like critical behavior, spanning several decades in the reduced temperature, could be observed. Our results convincingly show that the effective susceptibility exponent gamma_eff changes nonmonotonically from its classical to its Ising value when approaching the critical point in the ordered phase. In the disordered phase the behavior is monotonic. Furthermore the hypothesis that the crossover function is universal is supported.Comment: 4 pages RevTeX 3.0/3.1, 5 Encapsulated PostScript figures. Uses epsf.sty. Accepted for publication in Physical Review Letters. Also available as PostScript and PDF file at http://www.tn.tudelft.nl/tn/erikpubs.htm

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

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

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

Crossover scaling from classical to nonclassical critical behavior

We study the crossover between classical and nonclassical critical behaviors. The critical crossover limit is driven by the Ginzburg number G. The corresponding scaling functions are universal with respect to any possible microscopic mechanism which can vary G, such as changing the range or the strength of the interactions. The critical crossover describes the unique flow from the unstable Gaussian to the stable nonclassical fixed point. The scaling functions are related to the continuum renormalization-group functions. We show these features explicitly in the large-N limit of the O(N) phi^4 model. We also show that the effective susceptibility exponent is nonmonotonic in the low-temperature phase of the three-dimensional Ising model.Comment: 5 pages, final version to appear in Phys. Rev.

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.