Kinetics of domain growth in systems with local barriers

Crossover in growth law and violation of superuniversality in the random-field Ising model

We study the nonconserved phase-ordering dynamics of the d=2,3 random-field Ising model, quenched to below the critical temperature. Motivated by the puzzling results of previous work in two and three dimensions, reporting a crossover from power-law to logarithmic growth, together with superuniversal behavior of the correlation function, we have undertaken a careful investigation of both the domain growth law and the autocorrelation function. Our main results are as follows: We confirm the crossover to asymptotic logarithmic behavior in the growth law, but, at variance with previous findings, we find the exponent in the preasymptotic power law to be disorder dependent, rather than being that of the pure system. Furthermore, we find that the autocorrelation function does not display superuniversal behavior. This restores consistency with previous results for the d=1 system, and fits nicely into the unifying scaling scheme we have recently proposed in the study of the random-bond Ising model.

Naming games in two-dimensional and small-world-connected random geometric networks

We investigate a prototypical agent-based model, the naming game, on two-dimensional random geometric networks. The naming game [Baronchelli, J. Stat. Mech.: Theory Exp. (2006) P06014] is a minimal model, employing local communications that captures the emergence of shared communication schemes (languages) in a population of autonomous semiotic agents. Implementing the naming games with local broadcasts on random geometric graphs, serves as a model for agreement dynamics in large-scale, autonomously operating wireless sensor networks. Further, it captures essential features of the scaling properties of the agreement process for spatially embedded autonomous agents. Among the relevant observables capturing the temporal properties of the agreement process, we investigate the cluster-size distribution and the distribution of the agreement times, both exhibiting dynamic scaling. We also present results for the case when a small density of long-range communication links are added on top of the random geometric graph, resulting in a "small-world"-like network and yielding a significantly reduced time to reach global agreement. We construct a finite-size scaling analysis for the agreement times in this case.

Phase separation driven by surface diffusion: a Monte Carlo study

We propose a kinetic Ising model to study phase separation driven by surface diffusion. This model is referred to as Model S, and consists of the usual Kawasaki spin-exchange kinetics (Model B) in conjunction with a kinetic constraint. We use multispin coding techniques to develop fast algorithms for Monte Carlo simulations of Models B and S. We use these algorithms to study the late stages of pattern dynamics in these systems, and compare properties of the evolution morphologies, e.g., growth laws, domain distribution functions, and spatial and temporal correlation functions.

Autocorrelation functions for phase separation in ternary mixtures

We present numerical and analytical results for the autocorrelation functions which characterize domain growth in ternary mixtures. The numerical results are obtained from Monte Carlo simulations of the spin-1 Blume-Emery-Griffiths model with spin-exchange kinetics. Further, we model the autocorrelation functions using an approach based on the continuous-time random walk formalism. The aging property of these functions is related to the time dependence of the domain-size distribution. Our analytical results are found to be in good agreement with the numerical data.

Aging and equilibrium fluctuations for domain growth in ternary mixtures

We present numerical and analytical results for the autocorrelation functions which characterize domain growth in ternary mixtures. The numerical results are obtained from Monte Carlo studies of the spin-1 Blume-Emery-Griffiths model with spin-exchange kinetics. We formulate a stochastic model, which accounts for both aging and equilibrium contributions to the autocorrelation functions.

Dynamics of phase separation in multicomponent mixtures

We study the dynamics of phase separation in multicomponent mixtures through Monte Carlo simulations of the q-state Potts model with conserved kinetics. We use the Monte Carlo renormalization-group method to investigate the asymptotic regime. The domain growth law is found to be consistent with the Lifshitz-Slyozov law, L(t) equivalent to t(1/3) (where t is time), regardless of the value of q. We also present results for the scaled correlation functions and domain-size distribution functions for a range of q values.

Kinetics of phase separation in ternary mixtures

We present detailed results from Monte Carlo simulations of the kinetics of phase separation in ternary mixtures. We focus on the case of ABV mixtures (where V denotes a vacancy) and investigate segregation kinetics resulting from V-mediated dynamics. We provide heuristic arguments for the existence of different morphologies in various parameter regimes. Furthermore, we present comprehensive numerical results for various characteristic features of the domain growth process, e.g., real-space correlation functions, domain-size distribution functions, and growth laws.