8,820 research outputs found
Crossover scaling in two dimensions
We determine the scaling functions describing the crossover from Ising-like
critical behavior to classical critical behavior in two-dimensional systems
with a variable interaction range. Since this crossover spans several decades
in the reduced temperature as well as in the finite-size crossover variable, it
has up to now largely evaded a satisfactory numerical determination. Using a
new Monte Carlo method, we could obtain accurate results for sufficiently large
interactions ranges. Our data cover the full crossover region both above and
below the critical temperature and support the hypothesis that the crossover
functions are universal. Also the so-called effective exponents are discussed
and we show that these can vary nonmonotonically in the crossover region.Comment: 24 pages RevTeX 3.0/3.1, including 22 PostScript figures. Uses
epsf.st
Molecular-Dynamics Simulation of a Glassy Polymer Melt: Incoherent Scattering Function
We present simulation results for a model polymer melt, consisting of short,
nonentangled chains, in the supercooled state. The analysis focuses on the
monomer dynamics, which is monitored by the incoherent intermediate scattering
function. The scattering function is recorded over six decades in time and for
many different wave-vectors. The lowest temperatures studied are slightly above
the critical temperature of mode-coupling theory (MCT), which was determined
from a quantitative analysis of the beta- and alpha-relaxations. We find
evidence for the space-time factorization theorem in the beta-relaxation
regime, and for the time-temperature superposition principle in the
alpha-regime, if the temperature is not too close to the critical temperature.
The wave-vector dependence of the nonergodicity parameter, of the critical
amplitude, and the alpha-relaxation time are in qualitative agreement with
calculations for hard spheres. For wave-vectors larger than the maximum of the
structure factor the alpha-relaxation time already agrees fairly well with the
asymptotic MCT-prediction. The behavior of the relaxation time at small
wave-vectors can be rationalized by the validity of the Gaussian approximation
and the value of the Kohlrausch stretching exponent.Comment: 23 pages of REVTeX, 13 PostScript figures, submitted to Phys. Rev.
Finite-size scaling above the upper critical dimension revisited: The case of the five-dimensional Ising model
Monte Carlo results for the moments of the magnetization distribution
of the nearest-neighbor Ising ferromagnet in a L^d geometry, where L (4 \leq L
\leq 22) is the linear dimension of a hypercubic lattice with periodic boundary
conditions in d=5 dimensions, are analyzed in the critical region and compared
to a recent theory of Chen and Dohm (CD) [X.S. Chen and V. Dohm, Int. J. Mod.
Phys. C (1998)]. We show that this finite-size scaling theory (formulated in
terms of two scaling variables) can account for the longstanding discrepancies
between Monte Carlo results and the so-called ``lowest-mode'' theory, which
uses a single scaling variable tL^{d/2} where t=T/T_c-1 is the temperature
distance from the critical temperature, only to a very limited extent. While
the CD theory gives a somewhat improved description of corrections to the
``lowest-mode'' results (to which the CD theory can easily be reduced in the
limit t \to 0, L \to \infty, tL^{d/2} fixed) for the fourth-order cumulant,
discrepancies are found for the susceptibility (L^d ). Reasons for these
problems are briefly discussed.Comment: 9 pages, 13 Encapsulated PostScript figures. To appear in Eur. Phys.
J. B. Also available as PDF file at
http://www.cond-mat.physik.uni-mainz.de/~luijten/erikpubs.htm
A Monte Carlo study of surface critical phenomena: The special point
We study the special point in the phase diagram of a semi-infinite system,
where the bulk transition is in the three-dimensional Ising universality class.
To this end we perform a finite size scaling study of the improved Blume-Capel
model on the simple cubic lattice with two different types of surface
interactions. In order to check for the effect of leading bulk corrections we
have also simulated the spin-1/2 Ising model on the simple cubic lattice. We
have accurately estimated the surface enhancement coupling at the special point
of these models. We find and for the
surface renormalization group exponents of the special transitions. These
results are compared with previous ones obtained by using field theoretic
methods and Monte Carlo simulations of the spin-1/2 Ising model. Furthermore we
study the behaviour of the surface transition near the special point and
finally we discuss films with special boundary conditions at one surface and
fixed ones at the other.Comment: 21 pages, 2 figures. figure 1 replaced, various typos correcte
Structure of Polymer Brushes in Cylindrical Tubes: A Molecular Dynamics Simulation
Molecular Dynamics simulations of a coarse-grained bead-spring model of
flexible macromolecules tethered with one end to the surface of a cylindrical
pore are presented. Chain length and grafting density are varied
over a wide range and the crossover from ``mushroom'' to ``brush'' behavior is
studied for three pore diameters. The monomer density profile and the
distribution of the free chain ends are computed and compared to the
corresponding model of polymer brushes at flat substrates. It is found that
there exists a regime of and for large enough pore diameter where
the brush height in the pore exceeds the brush height on the flat substrate,
while for large enough and (and small enough pore diameters) the
opposite behavior occurs, i.e. the brush is compressed by confinement. These
findings are used to discuss the corresponding theories on polymer brushes at
concave substrates.Comment: 11 figure
Orthorhombic Phase of Crystalline Polyethylene: A Monte Carlo Study
In this paper we present a classical Monte Carlo simulation of the
orthorhombic phase of crystalline polyethylene, using an explicit atom force
field with unconstrained bond lengths and angles and periodic boundary
conditions. We used a recently developed algorithm which apart from standard
Metropolis local moves employs also global moves consisting of displacements of
the center of mass of the whole chains in all three spatial directions as well
as rotations of the chains around an axis parallel to the crystallographic
c-direction. Our simulations are performed in the NpT ensemble, at zero
pressure, and extend over the whole range of temperatures in which the
orthorhombic phase is experimentally known to be stable (10 - 450 K). In order
to investigate the finite-size effects in this extremely anisotropic crystal,
we used different system sizes and different chain lengths, ranging from C_12
to C_96 chains, the total number of atoms in the super-cell being between 432
and 3456. We show here the results for structural parameters, such as the
orthorhombic cell parameters a,b,c, and the setting angle of the chains, as
well as internal parameters of the chains, such as the bond lengths and angles.
Among thermodynamic quantities, we present results for thermal expansion
coefficients, elastic constants and specific heat. We discuss the temperature
dependence of the measured quantities as well as the related finite-size
effects. In case of lattice parameters and thermal expansion coefficients, we
compare our results to those obtained from other theoretical approaches as well
as to some available experimental data. We also suggest some possible ways of
extending this study.Comment: 27 pages, RevTex, 24 figures, submitted to Journal of Chemical
Physic
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