21 research outputs found
Phase Transitions of Hard Disks in External Periodic Potentials: A Monte Carlo Study
The nature of freezing and melting transitions for a system of hard disks in
a spatially periodic external potential is studied using extensive Monte Carlo
simulations. Detailed finite size scaling analysis of various thermodynamic
quantities like the order parameter, its cumulants etc. are used to map the
phase diagram of the system for various values of the density and the amplitude
of the external potential. We find clear indication of a re-entrant liquid
phase over a significant region of the parameter space. Our simulations
therefore show that the system of hard disks behaves in a fashion similar to
charge stabilized colloids which are known to undergo an initial freezing,
followed by a re-melting transition as the amplitude of the imposed, modulating
field produced by crossed laser beams is steadily increased. Detailed analysis
of our data shows several features consistent with a recent dislocation
unbinding theory of laser induced melting.Comment: 36 pages, 16 figure
Spin glass behavior of frustrated 2-D Penrose lattice in the classical planar model
Via extensive Monte Carlo studies we show that the frustrated XY Hamiltonian
on a 2-D Penrose lattice admits of a spin glass phase at low temperature.
Studies of the Edwards-Anderson order parameter, spin glass susceptibility, and
local (linear) susceptibility point unequivocally to a paramagnetic to spin
glass transition as the temperature is lowered. Specific heat shows a rounded
peak at a temperature above the spin glass transition temperature, as is
commonly observed in spin glasses. Our results strongly suggest that the
critical point exponents are the same as obtained by Bhatt and Young in the
Ising model on a square lattice. However, unlike in the latter case,
the critical temperature is clearly finite (nonzero). The results imply that a
quasiperiodic 2-D array of superconducting grains in a suitably chosen
transverse magnetic field should behave as a superconducting glass at low
temperature.Comment: RevTex, 4 pages Including 4 figures. To appear in the June 1 1996
issue of Phys. Rev. B (Rapid Communications). Revised/replaced edition
contains an erratum at the end of the paper, also to appear in Phys. Rev.
Tragedy revisited
âFreedom in a commons brings ruin to all.â So argued ecologist Garrett Hardin in âThe Tragedy of the Commonsâ in the 13 December 1968 issue of Science (1). Hardin questioned society's ability to manage shared resources and avoid an environmentally and socially calamitous free-for-all. In the 50 years since, the essay has influenced discussions ranging from climate change (see page 1217) to evolution, from infectious disease to the internet, and has reached far beyond academic literatureâbut not without criticism. Considerable work, notably by Nobelist Elinor Ostrom (2), has challenged Hardin, particularly his emphasis on property rights and government regulatory leviathans as solutions. Instead, research has documented contexts, cases, and principles that reflect the ability of groups to collectively govern common resources. To mark this anniversary and celebrate the richness of research and practice around commons and cooperation, Science invited experts to share some contemporary views on such tragedies and how to avert them. âBrad Wibl
Crystallization of a classical two-dimensional electron system: Positional and orientational orders
Crystallization of a classical two-dimensional one-component plasma
(electrons interacting with the Coulomb repulsion in a uniform neutralizing
positive background) is investigated with a molecular dynamics simulation. The
positional and the orientational correlation functions are calculated for the
first time. We have found an indication that the solid phase has a
quasi-long-range (power-law) positional order along with a long-range
orientational order. This indicates that, although the long-range Coulomb
interaction is outside the scope of Mermin's theorem, the absence of ordinary
crystalline order at finite temperatures applies to the electron system as
well. The `hexatic' phase, which is predicted between the liquid and the solid
phases by the Kosterlitz-Thouless-Halperin-Nelson-Young theory, is also
discussed.Comment: 3 pages, 4 figures; Corrected typos; Double columne
Universality in the Screening Cloud of Dislocations Surrounding a Disclination
A detailed analytical and numerical analysis for the dislocation cloud
surrounding a disclination is presented. The analytical results show that the
combined system behaves as a single disclination with an effective fractional
charge which can be computed from the properties of the grain boundaries
forming the dislocation cloud. Expressions are also given when the crystal is
subjected to an external two-dimensional pressure. The analytical results are
generalized to a scaling form for the energy which up to core energies is given
by the Young modulus of the crystal times a universal function. The accuracy of
the universality hypothesis is numerically checked to high accuracy. The
numerical approach, based on a generalization from previous work by S. Seung
and D.R. Nelson ({\em Phys. Rev A 38:1005 (1988)}), is interesting on its own
and allows to compute the energy for an {\em arbitrary} distribution of
defects, on an {\em arbitrary geometry} with an arbitrary elastic {\em energy}
with very minor additional computational effort. Some implications for recent
experimental, computational and theoretical work are also discussed.Comment: 35 pages, 21 eps file
Topological Defects and Non-homogeneous Melting of Large 2D Coulomb Clusters
The configurational and melting properties of large two-dimensional clusters
of charged classical particles interacting with each other via the Coulomb
potential are investigated through the Monte Carlo simulation technique. The
particles are confined by a harmonic potential. For a large number of particles
in the cluster (N>150) the configuration is determined by two competing
effects, namely in the center a hexagonal lattice is formed, which is the
groundstate for an infinite 2D system, and the confinement which imposes its
circular symmetry on the outer edge. As a result a hexagonal Wigner lattice is
formed in the central area while at the border of the cluster the particles are
arranged in rings. In the transition region defects appear as dislocations and
disclinations at the six corners of the hexagonal-shaped inner domain. Many
different arrangements and type of defects are possible as metastable
configurations with a slightly higher energy. The particles motion is found to
be strongly related to the topological structure. Our results clearly show that
the melting of the clusters starts near the geometry induced defects, and that
three different melting temperatures can be defined corresponding to the
melting of different regions in the cluster.Comment: 7 pages, 11 figures, submitted to Phys. Rev.
Enhanced stability of the square lattice of a classical bilayer Wigner crystal
The stability and melting transition of a single layer and a bilayer crystal
consisting of charged particles interacting through a Coulomb or a screened
Coulomb potential is studied using the Monte-Carlo technique. A new melting
criterion is formulated which we show to be universal for bilayer as well as
for single layer crystals in the case of (screened) Coulomb, Lennard--Jones and
1/r^{12} repulsive inter-particle interactions. The melting temperature for the
five different lattice structures of the bilayer Wigner crystal is obtained,
and a phase diagram is constructed as a function of the interlayer distance. We
found the surprising result that the square lattice has a substantial larger
melting temperature as compared to the other lattice structures. This is a
consequence of the specific topology of the defects which are created with
increasing temperature and which have a larger energy as compared to the
defects in e.g. a hexagonal lattice.Comment: Accepted for publication in Physical Review
Hexatic-Herringbone Coupling at the Hexatic Transition in Smectic Liquid Crystals: 4- Renormalization Group Calculations Revisited
Simple symmetry considerations would suggest that the transition from the
smectic-A phase to the long-range bond orientationally ordered hexatic
smectic-B phase should belong to the XY universality class. However, a number
of experimental studies have constantly reported over the past twenty years
"novel" critical behavior with non-XY critical exponents for this transition.
Bruinsma and Aeppli argued in Physical Review Letters {\bf 48}, 1625 (1982),
using a renormalization-group calculation, that short-range
molecular herringbone correlations coupled to the hexatic ordering drive this
transition first order via thermal fluctuations, and that the critical behavior
observed in real systems is controlled by a `nearby' tricritical point. We have
revisited the model of Bruinsma and Aeppli and present here the results of our
study. We have found two nontrivial strongly-coupled herringbone-hexatic fixed
points apparently missed by those authors. Yet, those two new nontrivial
fixed-points are unstable, and we obtain the same final conclusion as the one
reached by Bruinsma and Aeppli, namely that of a fluctuation-driven first order
transition. We also discuss the effect of local two-fold distortion of the bond
order as a possible missing order parameter in the Hamiltonian.Comment: 1 B/W eps figure included. Submitted to Physical Review E. Contact:
[email protected]
Influence of uncorrelated overlayers on the magnetism in thin itinerant-electron films
The influence of uncorrelated (nonmagnetic) overlayers on the magnetic
properties of thin itinerant-electron films is investigated within the
single-band Hubbard model. The Coulomb correlation between the electrons in the
ferromagnetic layers is treated by using the spectral density approach (SDA).
It is found that the presence of nonmagnetic layers has a strong effect on the
magnetic properties of thin films. The Curie temperatures of very thin films
are modified by the uncorrelated overlayers. The quasiparticle density of
states is used to analyze the results. In addition, the coupling between the
ferromagnetic layers and the nonmagnetic layers is discussed in detail. The
coupling depends on the band occupation of the nonmagnetic layers, while it is
almost independent of the number of the nonmagnetic layers. The induced
polarization in the nonmagnetic layers shows a long-range decreasing
oscillatory behavior and it depends on the coupling between ferromagnetic and
nonmagnetic layers.Comment: 9 pages, RevTex, 6 figures, for related work see:
http://orion.physik.hu-berlin.d
Melting as a String-Mediated Phase Transition
We present a theory of the melting of elemental solids as a
dislocation-mediated phase transition. We model dislocations near melt as
non-interacting closed strings on a lattice. In this framework we derive simple
expressions for the melting temperature and latent heat of fusion that depend
on the dislocation density at melt. We use experimental data for more than half
the elements in the Periodic Table to determine the dislocation density from
both relations. Melting temperatures yield a dislocation density of (0.61\pm
0.20) b^{-2}, in good agreement with the density obtained from latent heats,
(0.66\pm 0.11) b^{-2}, where b is the length of the smallest
perfect-dislocation Burgers vector. Melting corresponds to the situation where,
on average, half of the atoms are within a dislocation core.Comment: 18 pages, LaTeX, 3 eps figures, to appear in Phys. Rev.