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Investigation of metastable states and nucleation in the kinetic Ising model
Kurt Binder,H. Müller-Krumbhaar +1 more
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In this paper, the authors studied the relaxation of a two-dimensional Ising ferromagnet after a sudden reversal of the applied magnetic field from various points of view, including nucleation theories, computer experiments and a scaling theory, to provide a description for the metastable states and the kinetics of the magnetization reversal.Abstract:
The relaxation of a two-dimensional Ising ferromagnet after a sudden reversal of the applied magnetic field is studied from various points of view, including nucleation theories, computer experiments, and a scaling theory, to provide a description for the metastable states and the kinetics of the magnetization reversal. Metastable states are characterized by a "flatness" property of the relaxation function. The Monte Carlo method is used to simulate the relaxation process for finite $L\ifmmode\times\else\texttimes\fi{}L$ square lattices ($L=55, 110, 220 \mathrm{and} 440, \mathrm{respectively}$); no dependence on $L$ is found for these systems in the range of magnetic fields calculated. The metastable states found for small enough fields terminate at a rather well-defined "coercive field," where no singular behavior of the susceptibility can be detected, within the accuracy of the numerical calculation. In order to explain these results an approximate theory of cluster dynamics is derived from the master equation, and Fisher's static-cluster model, generalizing the more conventional nucleation theories. It is shown that the properties of the metastable states (including their lifetimes) derived from this treatment are quite consistent with the numerical data, although the details of the dynamics of cluster distributions are somewhat different. This treatment contradicts the mean-field theory and other extrapolations, predicting the existence of a spinodal curve. In order to elucidate the possible analytic behavior of the coercive field we discuss a generalization of the scaling equation of state, which includes the metastable states in agreement with our data.read more
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Evolutionary games on graphs
György Szabó,Gábor Fáth +1 more
TL;DR: The major theme of the review is in what sense and how the graph structure of interactions can modify and enrich the picture of long term behavioral patterns emerging in evolutionary games.
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Theory of first-order phase transitions
TL;DR: In this paper, a review of various concepts about first-order phase transitions is given, with particular emphasis on metastable states near first order phase transitions, on the'stability limits' of such states (e.g., the spinodal curve of the gas-liquid transition) and on the dynamic mechanisms by which metastable state decay (nucleation and growth of droplets of a new phase).
Journal ArticleDOI
Statistical theory of nucleation, condensation and coagulation
Kurt Binder,Dietrich Stauffer +1 more
TL;DR: In this article, the authors derive theories for nucleation, coagulation and droplet growth by reformulating the dynamics in terms of "clusters" and show that these theories agree quantitatively with computer simulations of the nucleation kinetics in the lattice gas model, and also give a much better account of recent nucleation experiments on CO2.
Journal ArticleDOI
Microscopic Evidence for Liquid-Liquid Separation in Supersaturated CaCO3 Solutions
Adam F. Wallace,Adam F. Wallace,Lester O. Hedges,Alejandro Fernandez-Martinez,Alejandro Fernandez-Martinez,Paolo Raiteri,Julian D. Gale,Glenn A. Waychunas,Stephen Whitelam,Jillian F. Banfield,Jillian F. Banfield,James J. De Yoreo,James J. De Yoreo +12 more
TL;DR: This study uses molecular dynamics simulations to probe the structure, dynamics, and energetics of hydrated CaCO3 clusters and lattice gas simulations to explore the behavior of cluster populations before nucleation and predicts formation of a dense liquid phase through liquid-liquid separation within the concentration range in which clusters are observed.
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Nonlinear aspects of the Cahn-Hilliard equation
Amy Novick-Cohen,Lee A. Segel +1 more
TL;DR: In this paper, a comparison theorem for stability criteria which was postulated by Langer is proved in the framework of the natural boundary conditions, and the full set of equilibrium solutions is specified.
References
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Journal ArticleDOI
Equation of state calculations by fast computing machines
TL;DR: In this article, a modified Monte Carlo integration over configuration space is used to investigate the properties of a two-dimensional rigid-sphere system with a set of interacting individual molecules, and the results are compared to free volume equations of state and a four-term virial coefficient expansion.
Journal ArticleDOI
Free Energy of a Nonuniform System. I. Interfacial Free Energy
John W. Cahn,John E. Hilliard +1 more
TL;DR: In this article, it was shown that the thickness of the interface increases with increasing temperature and becomes infinite at the critical temperature Tc, and that at a temperature T just below Tc the interfacial free energy σ is proportional to (T c −T) 3 2.
Journal ArticleDOI
Crystal statistics. I. A two-dimensional model with an order-disorder transition
TL;DR: In this article, the eigenwert problem involved in the corresponding computation for a long strip crystal of finite width, joined straight to itself around a cylinder, is solved by direct product decomposition; in the special case $n=\ensuremath{\infty}$ an integral replaces a sum.
Journal ArticleDOI
Time‐Dependent Statistics of the Ising Model
TL;DR: In this paper, the effect of a uniform, time-varying magnetic field upon the Ising model is discussed, and the frequency-dependent magnetic susceptibility is found in the weak-field limit.
Journal ArticleDOI
On spinodal decomposition
TL;DR: In this article, the stability of a solid solution to all infinitesimal composition fluctuations is considered, taking surface tension and elastic energy into account, and it is found that for infinite isotropic solids, free from imperfections, the spinodal marks the limit of metastability to such fluctuations only if there is no change in molar volume with composition.