44 research outputs found
Domain Growth and Finite-Size-Scaling in the Kinetic Ising Model
This paper describes the application of finite-size scaling concepts to
domain growth in systems with a non-conserved order parameter. A finite-size
scaling ansatz for the time-dependent order parameter distribution function is
proposed, and tested with extensive Monte-Carlo simulations of domain growth in
the 2-D spin-flip kinetic Ising model. The scaling properties of the
distribution functions serve to elucidate the configurational self-similarity
that underlies the dynamic scaling picture. Moreover, it is demonstrated that
the application of finite-size-scaling techniques facilitates the accurate
determination of the bulk growth exponent even in the presence of strong
finite-size effects, the scale and character of which are graphically exposed
by the order parameter distribution function. In addition it is found that one
commonly used measure of domain size--the scaled second moment of the
magnetisation distribution--belies the full extent of these finite-size
effects.Comment: 13 pages, Latex. Figures available on request. Rep #9401
Monte Carlo Methods for Estimating Interfacial Free Energies and Line Tensions
Excess contributions to the free energy due to interfaces occur for many
problems encountered in the statistical physics of condensed matter when
coexistence between different phases is possible (e.g. wetting phenomena,
nucleation, crystal growth, etc.). This article reviews two methods to estimate
both interfacial free energies and line tensions by Monte Carlo simulations of
simple models, (e.g. the Ising model, a symmetrical binary Lennard-Jones fluid
exhibiting a miscibility gap, and a simple Lennard-Jones fluid). One method is
based on thermodynamic integration. This method is useful to study flat and
inclined interfaces for Ising lattices, allowing also the estimation of line
tensions of three-phase contact lines, when the interfaces meet walls (where
"surface fields" may act). A generalization to off-lattice systems is described
as well.
The second method is based on the sampling of the order parameter
distribution of the system throughout the two-phase coexistence region of the
model. Both the interface free energies of flat interfaces and of (spherical or
cylindrical) droplets (or bubbles) can be estimated, including also systems
with walls, where sphere-cap shaped wall-attached droplets occur. The
curvature-dependence of the interfacial free energy is discussed, and estimates
for the line tensions are compared to results from the thermodynamic
integration method. Basic limitations of all these methods are critically
discussed, and an outlook on other approaches is given