Search results for "ISING"
showing 10 items of 1141 documents
From capillary condensation to interface localization transitions in colloid-polymer mixtures confined in thin-film geometry.
2008
Monte Carlo simulations of the Asakura-Oosawa (AO) model for colloid-polymer mixtures confined between two parallel repulsive structureless walls are presented and analyzed in the light of current theories on capillary condensation and interface localization transitions. Choosing a polymer to colloid size ratio of q=0.8 and studying ultrathin films in the range of D=3 to D=10 colloid diameters thickness, grand canonical Monte Carlo methods are used; phase transitions are analyzed via finite size scaling, as in previous work on bulk systems and under confinement between identical types of walls. Unlike the latter work, inequivalent walls are used here: while the left wall has a hard-core rep…
Dipolar order and disorder phenomena in pure CO and dilute (CO)1−x(Ar)x mixtures physisorbed on graphite
1999
Abstract A detailed heat capacity study has been performed to characterize the properties of pure CO and (CO) 1− x (Ar) x mixture films physisorbed on the basal planes of graphite. The phase diagram of CO monolayers will be presented. At T c =5.18 K a phase transition to a novel low temperature phase is found with head-tail (dipolar) order of the molecules in an orientationally ordered herringbone structure. The phase transition is shown to belong to the 2D Ising universality class with anisotropic interactions between the molecules. Diluting CO weakly with Ar impurities leads to a dramatic destruction of the phase transition. This effect can be quantitatively described by the 2D random fie…
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…
Monte Carlo investigation of head-tail ordering of CO monolayers on graphite
1994
Abstract Heat capacity measurements recently showed that CO physisorbed on graphite undergoes a head-tail ordering transition at roughly 5 K. The present paper is a detailed Monte Carlo study of this phase transition and the ordered state. The simulations are based on an ab initio pair potential and rely crucially on a thorough finite-size scaling study of various quantities. In agreement with experiments we find that the transition belongs to the universality class of the Ising model in two dimensions. We go beyond experimental knowledge by revealing the particular ferrielectric structure of the ground state, and show that the transition is due to the molecule's shape asymmetry rather than…
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…
Monte Carlo study of the ising model phase transition in terms of the percolation transition of “physical clusters”
1990
Finite squareL×L Ising lattices with ferromagnetic nearest neighbor interaction are simulated using the Swendsen-Wang cluster algorithm. Both thermal properties (internal energyU, specific heatC, magnetization 〈|M|〉, susceptibilityχ) and percolation cluster properties relating to the “physical clusters,” namely the Fortuin-Kasteleyn clusters (percolation probability 〈P∞〉, percolation susceptibilityχp, cluster size distributionnl) are evaluated, paying particular attention to finite-size effects. It is shown that thermal properties can be expressed entirely in terms of cluster properties, 〈P∞〉 being identical to 〈|M|〉 in the thermodynamic limit, while finite-size corrections differ. In contr…
Observation of random-field behavior in (CO)1−x(N2)xmixtures physisorbed on graphite
1993
Heat-capacity studies have been carried out on submonolayers of (CO${)}_{1\mathrm{\ensuremath{-}}\mathit{x}}$(${\mathrm{N}}_{2}$${)}_{\mathit{x}}$ mixtures physisorbed on graphite. We find that pure CO undergoes an end-to-end ordering transition at ${\mathit{T}}_{\mathit{c}}$=5.18 K, which is shown to belong to the two-dimensional Ising universality class. In diluting CO with ${\mathrm{N}}_{2}$ the heat-capacity peaks become progressively rounded until the phase transition is completely suppressed at a ${\mathrm{N}}_{2}$ concentration of only x=0.07. The analysis of the data shows that this behavior is in quantitative agreement with predictions of the random-field theory applied to adsorbed…
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
Analytical solution of 1D Ising-like systems modified by weak long range interaction
1999
It is well-known that 1D systems with only nearest neighbour interaction exhibit no phase transition. It is shown that the presence of a small long range interaction treated by the mean field approximation in addition to strong nearest neighbour interaction gives rise to hysteresis curves of large width. This situation is believed to exist in spin crossover systems where by the deformation of the spin changing molecules, an elastic coupling leads to a long range interaction, and strong bonding between the molecules in a chain compound leads to large values for nearest neighbour interaction constants. For this interaction scheme an analytical solution has been derived and the interplay betwe…