E. T. Gawlinski

Numerical simulation of models of ordering: scaling and growth laws

A summary of recent numerical simulations of ordering in several two-dimensional models is presented. Primary emphasis is given to simulations of domain growth in the kinetic Ising, Langevin and celldynamics models with conserved order parameters. The modified Lifshitz-Slyozov-Wagner domaingrowth law is found to be an excellent fit to the data in all cases. In addition, the nonequilibrium pair correlation functions are shown to satisfy the same universal scaling form. The structure factors are also shown to satisfy dynamical scaling. Thus all three models are shown to belong to the same dynamical universality class, for the range of space and time considered in these studies.

Numerical Simulation Studies of the Kinetics of First Order Phase Transitions

Numerical simulation methods have a rich history in the study of the kinetics of first order phase transitions 1. These include Monte Carlo and molecular dynamics simulations and numerical integration of stochastic differential equations, some of which will be discussed in this article. It has been recognized for many years that such studies are useful in obtaining qualitative insights, such as the role of conservation laws, vertices, dimensionality, etc. in ordering processes. However, it is quite difficult to determine asymptotic domain growth laws for bulk systems by such methods, due both to finite size effects and related finite time limitations imposed by current computer capabilities2. It is particularly difficult to determine growth laws and scaling functions for problems in which one has no theoretical prediction to test. Similar difficulties exist for experimentalists, of course! Recent theoretical developments, however, have led to renewed interest in determining the growth law for systems which undergo spinodal decomposition and coarsening, such as occurs following a quench below a critical point at a critical value of the order parameter. We will primarily focus on this issue here, given its importance in understanding phase-separation dynamics in two and three dimensional systems. Huse3 has recently given a heuristic argument that for such a quench the asymptotic domain growth behavior is described by a Lifshitz-Slyozov exponent, i.e. the characteristic length, L(t), behaves like L(t) ~ tx, with x = 1/3.

COMPUTER SIMULATIONS OF DOMAIN GROWTH

A review is given of the use of lattice gas models to simulate the kinetics of first-order phase transitions. In particular we discuss domain growth in the non-conserved Ising model, a prototypical example which simulates, for example, the order-disorder transition in binary alloys. Other models will also be discussed.

RANDOM FIELD ISING MODEL: COMPUTER SIMULATIONS OF DOMAIN GROWTH

We have simulated the two-dimensional ferromagnetic Ising model in a random magnetic field with spin-flip dynamics. After the system is deeply quenched into the unstable region of the zero-field phase diagram, we observe novel dynamical behaviour for the average size of the growing domains. Recent theoretical predictions are discussed.