The unusual thermodynamic properties of the Ising antiferromagnet supplemented with a ferromagnetic, mean-field term are outlined. This simple model is inspired by more realistic models of spin-crossover materials. The phase diagram is estimated usin
g Metropolis Monte Carlo methods, and differences with preliminary Wang-Landau Monte Carlo results for small systems are noted.
The dynamics of desorption from a submonolayer of adsorbed atoms or ions are significantly influenced by the absence or presence of lateral diffusion of the adsorbed particles. When diffusion is present, the adsorbate configuration is simultaneously
changed by two distinct processes, proceeding in parallel: adsorption/desorption, which changes the total adsorbate coverage, and lateral diffusion, which is coverage conserving. Inspired by experimental results, we here study the effects of these competing processes by kinetic Monte Carlo simulations of a simple lattice-gas model. In order to untangle the various effects, we perform large-scale simulations, in which we monitor coverage, correlation length, and cluster-size distributions, as well as the behavior of representative individual clusters, during desorption. For each initial adsorbate configuration, we perform multiple, independent simulations, without and with diffusion, respectively. We find that, compared to desorption without diffusion, the coverage-conserving diffusion process produces two competing effects: a retardation of the desorption rate, which is associated with a coarsening of the adsorbate configuration, and an acceleration due to desorption of monomers evaporated from the cluster perimeters. The balance between these two effects is governed by the structure of the adsorbate layer at the beginning of the desorption process. Deceleration and coarsening are predominant for configurations dominated by monomers and small clusters, while acceleration is predominant for configurations dominated by large clusters.
We present results of kinetic Monte Carlo simulations of a modified Ziff-Gulari-Barshad model for the reaction CO+O --> CO_2 on a catalytic surface. Our model includes impurities in the gas phase, CO desorption, and a modification known to eliminate
the unphysical O poisoned phase. The impurities can adsorb and desorb on the surface, but otherwise remain inert. In a previous work that did not include CO desorption [G. M. Buendia and P. A. Rikvold, Phys. Rev. E, 85 031143 (2012)], we found that the impurities have very distinctive effects on the phase diagram and greatly diminish the reactivity of the system. If the impurities do not desorb, once the system reaches a stationary state, the CO_2 production disappears. When the impurities are allowed to desorb, there are regions where the CO_2 reaction window reappears, although greatly reduced. Following experimental evidence that indicates that temperature effects are crucial in many catalytic processes, here we further analyze these effects by including a CO desorption rate. We find that the CO desorption has the effect to smooth the transition between the reactive and the CO rich phase, and most importantly it can counteract the negative effects of the presence of impurities by widening the reactive window such that now the system remains catalytically active in the whole range of CO pressures.
We report a preliminary numerical study by kinetic Monte Carlo simulation of the dynamics of phase separation following a quench from high to low temperature in a system with a single, conserved, scalar order parameter (a kinetic Ising ferromagnet) c
onfined to a hyperbolic lattice. The results are compared with simulations of the same system on two different, Euclidean lattices, in which cases we observe power-law domain growth with an exponent near the theoretically known value of 1/3. For the hyperbolic lattice we observe much slower domain growth, consistent to within our current accuracy with power-law growth with a much smaller exponent near 0.13. The paper also includes a brief introduction to non-Euclidean lattices and their mapping to the Euclidean plane.
Engineering networks fall into the category of large-scale networks with heterogeneous nodes such as sources and sinks. The survivability analysis of such networks requires the analysis of the connectivity of the network components for every possible
combination of faults to determine a network response to each combination of faults. From the computational complexity point of view, the problem belongs to the class of exponential time problems at least. Partially, the problem complexity can be reduced by mapping the initial topology of a complex large-scale network with multiple sources and multiple sinks onto a set of smaller sub-topologies with multiple sources and a single sink connected to the network of sources by a single link. In this paper, the mapping procedure is applied to the Florida power grid.
We study by kinetic Monte Carlo simulations the catalytic oxidation of carbon monoxide on a surface in the presence of contaminants in the gas phase. The process is simulated by a Ziff-Gulari-Barshad (ZGB) model that has been modified to include the
effect of the contaminants and to eliminate the unphysical oxygen-poisoned phase. The impurities can adsorb and desorb on the surface, but otherwise remain inert. We find that, if the impurities can not desorb, no matter how small their proportion in the gas mixture, the first order transition and the reactive window that characterize the ZGB model disappear. The coverages become continuous, and once the surface has reached a steady state there is no production of CO$_2$. This is quite different from the behavior of a system in which the surface presents a fixed percentage of impurities. When the contaminants are allowed to desorb, the reactive window appears again, and disappears at a value that depends on the proportion of contaminants in the gas and on their desorption rate.
We study the effect of coadsorption of CO and O on a Ziff-Gulari-Barshad (ZGB) model with CO desorption (ZGB-d) for the reaction CO + O --> CO_2 on a catalytic surface. Coadsorption of CO on a surface site already occupied by an O is introduced by an
Eley-Rideal-type mechanism that occurs with probability p, 0 <= p <= 1. We find that, besides the well known effect of eliminating the second-order phase transition between the reactive state and an O-poisoned state, the coadsorption step has a strong effect on the transition between the reactive state and the CO-poisoned state. The coexistence curve between these two states terminates at a critical value k_c of the desorption rate k which now depends on p. Our Monte Carlo simulations and finite-size scale analysis indicate that k_c decreases with increasing values of p. For p=1, there appears to be a sharp phase transition between the two states only for k at(or near) zero.
We study the dynamical response of a two-dimensional Ising model subject to a square-wave oscillating external field. In contrast to earlier studies, the system evolves under a so-called soft Glauber dynamic [P.A. Rikvold and M. Kolesik, J. Phys. A:
Math. Gen. 35, L117 (2002)], for which both nucleation and interface propagation are slower and the interfaces smoother than for the standard Glauber dynamic. We choose the temperature and magnitude of the external field such that the metastable decay of the system following field reversal occurs through nucleation and growth of many droplets of the stable phase, i.e., the multidroplet regime. Using kinetic Monte Carlo simulations, we find that the system undergoes a nonequilibrium phase transition, in which the symmetry-broken dynamic phase corresponds to an asymmetric stationary limit cycle for the time-dependent magnetization. The critical point is located where the half-period of the external field is approximately equal to the metastable lifetime of the system. We employ finite-size scaling analysis to investigate the characteristics of this dynamical phase transition. The critical exponents and the fixed-point value of the fourth-order cumulant are found to be consistent with the universality class of the two-dimensional equilibrium Ising model. As this universality class has previously been established for the same nonequilibrium model evolving under the standard Glauber dynamic, our results indicate that this far-from-equilibrium phase transition is universal with respect to the choice of the stochastic dynamics.
The nanoscopic structure and the stationary propagation velocity of (1+1)-dimensional solid-on-solid interfaces in an Ising lattice-gas model, which are driven far from equilibrium by an applied force, such as a magnetic field or a difference in (ele
ctro)chemical potential, are studied by an analytic nonlinear-response approximation together with kinetic Monte Carlo simulations. Here we consider the case that the system is coupled to a two-dimensional phonon bath. In the resulting dynamic, transitions that conserve the system energy are forbidden, and the effects of the applied force and the interaction energies do not factorize (a so-called hard dynamic). In full agreement with previous general theoretical results we find that the local interface width changes dramatically with the applied force. However, in contrast with other hard dynamics, this change is nonmonotonic in the driving force. However, significant differences between theory and simulation are found near two special values of the driving force, where certain transitions allowed by the solid-on-solid model become forbidden by the phonon-assisted dynamic. Our results represent a significant step toward providing a solid physical foundation for kinetic Monte Carlo simulations.
