11,264 research outputs found
Finite-size Scaling and Universality above the Upper Critical Dimensionality
According to renormalization theory, Ising systems above their upper critical
dimensionality d_u = 4 have classical critical behavior and the ratio of
magnetization moments Q = ^2 / has the universal value 0.456947...
However, Monte Carlo simulations of d = 5 Ising models have been reported which
yield strikingly different results, suggesting that the renormalization
scenario is incorrect. We investigate this issue by simulation of a more
general model in which d_u < 4, and a careful analysis of the corrections to
scaling. Our results are in a perfect agreement with the renormalization theory
and provide an explanation of the discrepancy mentioned.Comment: 5 pages RevTeX, 1 PostScript figure. Accepted for publication in
Physical Review Letter
Do crossover functions depend on the shape of the interaction profile?
We examine the crossover from classical to non-classical critical behaviour
in two-dimensional systems with a one-component order parameter. Since the
degree of universality of the corresponding crossover functions is still
subject to debate, we try to induce non-universal effects by adding
interactions with a second length scale. Although the crossover functions
clearly depend on the range of the interactions, they turn out to be remarkably
robust against further variation of the interaction profile. In particular, we
find that the earlier observed non-monotonic crossover of the effective
susceptibility exponent occurs for several qualitatively different shapes of
this profile.Comment: 7 pages + 4 PostScript figures. Accepted for publication in
Europhysics Letters. Also available as PDF file at
http://www.cond-mat.physik.uni-mainz.de/~luijten/erikpubs.htm
Reentrant transitions in colloidal or dusty plasma bilayers
The phase diagram of crystalline bilayers of particles interacting via a
Yukawa potential is calculated for arbitrary screening lengths and particle
densities. Staggered rectangular, square, rhombic and triangular structures are
found to be stable including a first-order transition between two different
rhombic structures. For varied screening length at fixed density, one of these
rhombic phases exhibits both a single and even a double reentrant transition.
Our predictions can be verified experimentally in strongly confined charged
colloidal suspensions or dusty plasma bilayers.Comment: 4 pages, 3 eps figs - revtex4. PRL - in pres
Domain Growth in Ising Systems with Quenched Disorder
We present results from extensive Monte Carlo (MC) simulations of domain
growth in ferromagnets and binary mixtures with quenched disorder. These are
modeled by the "random-bond Ising model" and the "dilute Ising model" with
either nonconserved (Glauber) spin-flip kinetics or conserved (Kawasaki)
spin-exchange kinetics. In all cases, our MC results are consistent with
power-law growth with an exponent which depends on the
quench temperature and the disorder amplitude . Such exponents
arise naturally when the coarsening domains are trapped by energy barriers
which grow logarithmically with the domain size. Our MC results show excellent
agreement with the predicted dependence of .Comment: 11 pages, 15 figure
Kinetics of Phase Separation in Thin Films: Simulations for the Diffusive Case
We study the diffusion-driven kinetics of phase separation of a symmetric
binary mixture (AB), confined in a thin-film geometry between two parallel
walls. We consider cases where (a) both walls preferentially attract the same
component (A), and (b) one wall attracts A and the other wall attracts B (with
the same strength). We focus on the interplay of phase separation and wetting
at the walls, which is referred to as {\it surface-directed spinodal
decomposition} (SDSD). The formation of SDSD waves at the two surfaces, with
wave-vectors oriented perpendicular to them, often results in a metastable
layered state (also referred to as ``stratified morphology''). This state is
reminiscent of the situation where the thin film is still in the one-phase
region but the surfaces are completely wet, and hence coated with thick wetting
layers. This metastable state decays by spinodal fluctuations and crosses over
to an asymptotic growth regime characterized by the lateral coarsening of
pancake-like domains. These pancakes may or may not be coated by precursors of
wetting layers. We use Langevin simulations to study this crossover and the
growth kinetics in the asymptotic coarsening regime.Comment: 39 pages, 19 figures, submitted to Phys.Rev.
Coupled Fluctuations near Critical Wetting
Recent work on the complete wetting transition has emphasized the role played
by the coupling of fluctuations of the order parameter at the wall and at the
depinning fluid interface. Extending this approach to the wetting transition
itself we predict a novel crossover effect associated with the decoupling of
fluctuations as the temperature is lowered towards the transition temperature
T_W. Using this we are able to reanalyse recent Monte-Carlo simulation studies
and extract a value \omega(T_W)=0.8 at T_W=0.9T_C in very good agreement with
long standing theoretical predictions.Comment: 4 pages, LaTex, 1 postscript figur
- …