Journal ArticleDOI
Monte Carlo study of growth in the two-dimensional spin-exchange kinetic Ising model
TLDR
In this paper, the authors presented results obtained from extensive Monte Carlo simulations of domain growth in the two-dimensional spin-exchange kinetic Ising model with equal numbers of up and down spins.Abstract:
Results obtained from extensive Monte Carlo simulations of domain growth in the two-dimensional spin-exchange kinetic Ising model with equal numbers of up and down spins are presented. Using different measures of domain size---including the pair-correlation function, the energy, and circularly-averaged structure factor---the domain size is determined (at T=0.5${T}_{c}$) as a function of time for times up to ${10}^{6}$ Monte Carlo steps. The growth law R(t)=A+${\mathrm{Bt}}^{1/3}$ is found to provide an excellent fit (within 0.3%) to the data, thus indicating that at long times the classical value of (1/3 for the exponent is correct. It is pointed out that this growth law is equivalent to an effective exponent for all times (as given by Huse) ${n}_{\mathrm{eff}}$(t)=(1/3-1)/3 C/R(t). No evidence for logarithmic behavior is seen. The self-averaging properties of the various measures of domain size and the variation of the constants A and B with temperature are also discussed. In addition, the scaling of the structure factor and anisotropy effects due to the lattice are examined.read more
Citations
More filters
Journal ArticleDOI
Theory of phase-ordering kinetics
TL;DR: The theory of phase-ordering dynamics that is the growth of order through domain coarsening when a system is quenched from the homogeneous phase into a broken-symmetry phase, with the emphasis on recent developments, is reviewed in this paper.
Journal ArticleDOI
Clustering on surfaces
TL;DR: In this paper, the authors summarize the current theoretical and experimental understanding of clustering phenomena on surfaces, with an emphasis on dynamical properties, including surface diffusion coefficients and adatom binding energies.
Journal ArticleDOI
Applications of Monte Carlo methods to statistical physics
TL;DR: An introductory review of the Monte Carlo method for the statistical mechanics of condensed matter systems is given in this paper, where basic principles (random number generation, simple sampling versus importance sampling, Markov chains and master equations) are explained and some classical applications (self-avoiding walks, percolation, the Ising model) are sketched.
Journal ArticleDOI
Spinodal decomposition of a symmetric critical mixture of deuterated and protonated polymer
Frank S. Bates,Pierre Wiltzius +1 more
TL;DR: In this article, a nearly symmetric critical mixture of perdeuterated and protonated 1,4 polybutadiene exhibiting an upper critical solution temperature Tc=61.5±1.5°C has been quenched from the homogeneous state (≂75 °C) to various temperatures between 25 and 57.5
Reference BookDOI
Kinetics of Phase Transitions
TL;DR: In this paper, the evolution of a homogeneous multi-component mixture which has been rendered thermodynamically unstable by a rapid quench below the critical temperature is reviewed, and results for cases with both nonconserved and conserved order parameters are discussed.