Search results for "Scaling"
showing 10 items of 754 documents
Statistical and systematic errors in Monte Carlo sampling
1991
We have studied the statistical and systematic errors which arise in Monte Carlo simulations and how the magnitude of these errors depends on the size of the system being examined when a fixed amount of computer time is used. We find that, depending on the degree of self-averaging exhibited by the quantities measured, the statistical errors can increase, decrease, or stay the same as the system size is increased. The systematic underestimation of response functions due to the finite number of measurements made is also studied. We develop a scaling formalism to describe the size dependence of these errors, as well as their dependence on the “bin length” (size of the statistical sample), both…
Optimized analysis of the critical behavior in polymer mixtures from Monte Carlo simulations
1992
A complete outline is given for how to determine the critical properties of polymer mixtures with extrapolation methods similar to the Ferrenberg-Swendsen techniques recently devised for spin systems. By measuring not only averages but the whole distribution of the quantities of interest, it is possible to extrapolate the data obtained in only a few simulations nearT c over the entire critical region, thereby saving at least 90% of the computer time normally needed to locate susceptibility peaks or cumulant intersections and still getting more precise results. A complete picture of the critical properties of polymer mixtures in the thermodynamic limit is then obtained with finite-size scali…
Simulation of the glass transition in polymeric systems: Evidence for an underlying phase transition?
1998
Abstract The bond fluctuation model of polymer chains on sc lattices with an energy that favours long bonds can describe the slowing down of supercooled melts that approach the glass transition in qualitative similarity with various experiments. In this paper we focus on the question of whether there exists a correlation length that increases to large values when the temperature is lowered towards the glass transition. Two types of analysis are presented: firstly density oscillations near hard walls become long range, and the resulting correlation length becomes larger than the gyration radius, secondly oscillations in the pair correlation function in real space also become long range, and …
Phase Transitions in Dense Lipid Monolayers Grafted to a Surface: Monte Carlo Investigation of a Coarse-Grained Off-Lattice Model
1996
Semiflexible amphiphilic molecules end-grafted at a flat surface are modeled by a bead-spring chain with stiff bond angle potentials. Constant density Monte Carlo simulations are performed varying temperature, density, and chain length of the molecules, whose effective monomers interact with Lennard-Jones potentials. For not too large densities and low temperatures the monolayer is in a quasi-two-dimensional crystalline state, characterized by uniform tilt of the (stretched) chains. Raising the temperature causes a second-order transition into a (still solid) phase with no tilt. For the first time, finite size scaling concepts are applied to a model of a surfactant monolayer, and it is foun…
Monte Carlo simulations of Ising models and polymer blends in double wedge geometry: Evidence for novel types of critical phenomena
2005
Abstract Two-phase coexistence in systems with free surfaces is enforced by boundary fields requiring the presence of an interface. Varying the temperature or the surface field, one can observe new types of phase transitions where the interface essentially disappears (it becomes bound to a wall or a wedge or a corner of the system). These transitions are simulated with Monte Carlo for Ising ferromagnets and polymer blends, applying finite size scaling analysis. Anisotropic critical fluctuations may occur, and in the limit where the system becomes macroscopically large in all three directions the order parameter vanishes discontinuously (either because its exponent β = 0 , or its critical am…
Mechanisms for the Dynamics of Phase Transformations
1984
An introductory review of the dynamics of (first- order) phase transitions is given. Concepts describing the initial stages of the transition, such as nucleation, spinodal decomposition (in the case of unmixing) are introduced, and their validity is critically discussed. The theoretical results are compared to recent computer simulations and pertinent experiments. Then the scaling concepts describing the late stages of domain growth are discussed, and open problems are outlined.
The crossover from first to second-order finite-size scaling: a numerical study
1994
We consider a particular case of the two dimensional Blume-Emery-Griffiths model to study the finite-size scaling for a field driven first-order phase transition with two coexisting phases not related by a symmetry. For low temperatures we verify the asymptotic (large volume) predictions of the rigorous theory of Borgs and Kotecky. Near the critical temperature we show that all data fit onto a unique curve, even when the correlation length ξ becomes comparable to or larger than the size of the system, provided the linear dimension L of the system is rescaled by ξ
Monte Carlo simulation of a lyotropic first-order isotropic-nematic phase transition in a lattice polymer model
1999
We present a Monte Carlo simulation of the bond-fluctuation lattice model, using a Hamiltonian which introduces a change in the conformational statistics of the polymer chains from Gaussian behavior at high temperatures to rigid rod behavior at low temperatures. We do not introduce any attractive interaction between the chains. Upon cooling, the aspect ratio of the chains increases above the critical value for the density employed in the simulation, and we observe an entropically driven phase transition into a nematic phase. We examine this transition quantitatively by a careful finite size scaling study using an optimized cumulant intersection method, and show that the transition is of fir…
Monte Carlo simulations of phase transitions of systems in nanoscopic confinement
2007
Abstract When simple or complex fluids are confined to ultrathin films or channels or other cavities of nanoscopic linear dimensions, the interplay of finite size and surface controls the phase behavior, and may lead to phase transitions rather different from the corresponding phenomena in the bulk. Monte Carlo simulation is a very suitable tool to clarify the complex behavior of such systems, since the boundary conditions providing the confinement can be controlled and arbitrarily varied, and detailed structural information on the inhomogeneous states of the considered systems is available. Examples used to illustrate these concepts include simple Ising models in pores and double-pyramid-s…
Path-Integral Monte Carlo Simulation for H2 and D2 Adsorbed on Graphite
1997
Molecular layers are very good realizations of two dimensional systems. Hydrogen molecules H 2,HD,D 2 adsorbed on graphite are excellent model systems for investigating the influence of substrate fields and of quantum effects on phase transitions. At a coverage of a complete commensurable layer in the √3 x √3 R30° structure experiments showed an anomalous effect, the system with the lighter H 2 molecules has a higher order-disorder transition temperature compared to the system with the heavier D 2 molecules. By a combination of path integral Monte Carlo and finite size scaling techniques we analyze this effect. In detail we study the order parameter and the cumulants and discuss the impact …