80 research outputs found
First and second order clustering transitions for a system with infinite-range attractive interaction
We consider a Hamiltonian system made of classical particles moving in
two dimensions, coupled via an {\it infinite-range interaction} gauged by a
parameter . This system shows a low energy phase with most of the particles
trapped in a unique cluster. At higher energy it exhibits a transition towards
a homogenous phase. For sufficiently strong coupling an intermediate phase
characterized by two clusters appears. Depending on the value of the
observed transitions can be either second or first order in the canonical
ensemble. In the latter case microcanonical results differ dramatically from
canonical ones. However, a canonical analysis, extended to metastable and
unstable states, is able to describe the microcanonical equilibrium phase. In
particular, a microcanonical negative specific heat regime is observed in the
proximity of the transition whenever it is canonically discontinuous. In this
regime, {\it microcanonically stable} states are shown to correspond to {\it
saddles} of the Helmholtz free energy, located inside the spinodal region.Comment: 4 pages, Latex - 3 EPS Figs - Submitted to Phys. Rev.
On the inequivalence of statistical ensembles
We investigate the relation between various statistical ensembles of finite
systems. If ensembles differ at the level of fluctuations of the order
parameter, we show that the equations of states can present major differences.
A sufficient condition for this inequivalence to survive at the thermodynamical
limit is worked out. If energy consists in a kinetic and a potential part, the
microcanonical ensemble does not converge towards the canonical ensemble when
the partial heat capacities per particle fulfill the relation
.Comment: 4 pages, 4 figure
Anomalous diffusion as a signature of collapsing phase in two dimensional self-gravitating systems
A two dimensional self-gravitating Hamiltonian model made by
fully-coupled classical particles exhibits a transition from a collapsing phase
(CP) at low energy to a homogeneous phase (HP) at high energy. From a dynamical
point of view, the two phases are characterized by two distinct single-particle
motions : namely, superdiffusive in the CP and ballistic in the HP. Anomalous
diffusion is observed up to a time that increases linearly with .
Therefore, the finite particle number acts like a white noise source for the
system, inhibiting anomalous transport at longer times.Comment: 10 pages, Revtex - 3 Figs - Submitted to Physical Review
Classification of phase transitions in small systems
We present a classification scheme for phase transitions in finite systems
like atomic and molecular clusters based on the Lee-Yang zeros in the complex
temperature plane. In the limit of infinite particle numbers the scheme reduces
to the Ehrenfest definition of phase transitions and gives the right critical
indices. We apply this classification scheme to Bose-Einstein condensates in a
harmonic trap as an example of a higher order phase transitions in a finite
system and to small Ar clusters.Comment: 12 pages, 4 figures, accepted for publication in Phys. Rev. Let
The Approach to Ergodicity in Monte Carlo Simulations
The approach to the ergodic limit in Monte Carlo simulations is studied using
both analytic and numerical methods. With the help of a stochastic model, a
metric is defined that enables the examination of a simulation in both the
ergodic and non-ergodic regimes. In the non-ergodic regime, the model implies
how the simulation is expected to approach ergodic behavior analytically, and
the analytically inferred decay law of the metric allows the monitoring of the
onset of ergodic behavior. The metric is related to previously defined measures
developed for molecular dynamics simulations, and the metric enables the
comparison of the relative efficiencies of different Monte Carlo schemes.
Applications to Lennard-Jones 13-particle clusters are shown to match the model
for Metropolis, J-walking and parallel tempering based approaches. The relative
efficiencies of these three Monte Carlo approaches are compared, and the decay
law is shown to be useful in determining needed high temperature parameters in
parallel tempering and J-walking studies of atomic clusters.Comment: 17 Pages, 7 Figure
The potential energy landscape of a model glass former: thermodynamics, anharmonicities, and finite size effects
It is possible to formulate the thermodynamics of a glass forming system in
terms of the properties of inherent structures, which correspond to the minima
of the potential energy and build up the potential energy landscape in the
high-dimensional configuration space. In this work we quantitatively apply this
general approach to a simulated model glass-forming system. We systematically
vary the system size between N=20 and N=160. This analysis enables us to
determine for which temperature range the properties of the glass former are
governed by the regions of the configuration space, close to the inherent
structures. Furthermore, we obtain detailed information about the nature of
anharmonic contributions. Moreover, we can explain the presence of finite size
effects in terms of specific properties of the energy landscape. Finally,
determination of the total number of inherent structures for very small systems
enables us to estimate the Kauzmann temperature
Curvature fluctuations and Lyapunov exponent at Melting
We calculate the maximal Lyapunov exponent in constant-energy molecular
dynamics simulations at the melting transition for finite clusters of 6 to 13
particles (model rare-gas and metallic systems) as well as for bulk rare-gas
solid. For clusters, the Lyapunov exponent generally varies linearly with the
total energy, but the slope changes sharply at the melting transition. In the
bulk system, melting corresponds to a jump in the Lyapunov exponent, and this
corresponds to a singularity in the variance of the curvature of the potential
energy surface. In these systems there are two mechanisms of chaos -- local
instability and parametric instability. We calculate the contribution of the
parametric instability towards the chaoticity of these systems using a recently
proposed formalism. The contribution of parametric instability is a continuous
function of energy in small clusters but not in the bulk where the melting
corresponds to a decrease in this quantity. This implies that the melting in
small clusters does not lead to enhanced local instability.Comment: Revtex with 7 PS figures. To appear in Phys Rev
Thermodynamics of Na_8 and Na_{20} clusters studied with ab-initio electronic structure methods
We study the thermodynamics of Na_8 and Na_{20} clusters using
multiple-histogram methods and an ab initio treatment of the valence electrons
within density functional theory. We consider the influence of various electron
kinetic-energy functionals and pseudopotentials on the canonical ionic specific
heats. The results for all models we consider show qualitative similarities,
but also significant temperature shifts from model to model of peaks and other
features in the specific-heat curves. The use of phenomenological
pseudopotentials shifts the melting peak substantially (~ 50--100 K) when
compared to ab-initio results. It is argued that the choice of a good
pseudopotential and use of better electronic kinetic-energy functionals has the
potential for performing large time scale and large sized thermodynamical
simulations on clusters.Comment: LaTeX file and EPS figures. 24 pages, 13 figures. Submitted to Phys.
Rev.
Melting behavior of ultrathin titanium nanowires
The thermal stability and melting behavior of ultrathin titanium nanowires
with multi-shell cylindrical structures are studied using molecular dynamic
simulation. The melting temperatures of titanium nanowires show remarkable
dependence on wire sizes and structures. For the nanowire thinner than 1.2 nm,
there is no clear characteristic of first-order phase transition during the
melting, implying a coexistence of solid and liquid phases due to finite size
effect. An interesting structural transformation from helical multi-shell
cylindrical to bulk-like rectangular is observed in the melting process of a
thicker hexagonal nanowire with 1.7 nm diameter.Comment: 4 pages, 4 figure
Thermodynamics of tin clusters
We report the results of detailed thermodynamic investigations of the
Sn cluster using density-functional molecular dynamics. These
simulations have been performed over a temperature range of 150 to 3000 K, with
a total simulation time of order 1 ns. The prolate ground state and low-lying
isomers consist of two tricapped trigonal prism (TTP) units stacked end to end.
The ionic specific heat, calculated via a multihistogram fit, shows a small
peak around 500 K and a shoulder around 850 K. The main peak occurs around 1200
K, about 700 K higher than the bulk melting temperature, but significantly
lower than that for Sn. The main peak is accompanied by a sharp change
in the prolate shape of the cluster due to the fusion of the two TTP units to
form a compact, near spherical structure with a diffusive liquidlike ionic
motion. The small peak at 500 K is associated with rearrangement processes
within the TTP units, while the shoulder at 850 K corresponds to distortion of
at least one TTP unit, preserving the overall prolate shape of the cluster. At
all temperatures observed, the bonding remains covalent.Comment: Latex File and EPS Figures. 18 pages,11 Figures. Submitted to Phys.
Rev.
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