56 research outputs found
Ordering and Demixing Transitions in Multicomponent Widom-Rowlinson Models
We use Monte Carlo techniques and analytical methods to study the phase
diagram of multicomponent Widom-Rowlinson models on a square lattice: there are
M species all with the same fugacity z and a nearest neighbor hard core
exclusion between unlike particles. Simulations show that for M between two and
six there is a direct transition from the gas phase at z < z_d (M) to a demixed
phase consisting mostly of one species at z > z_d (M) while for M \geq 7 there
is an intermediate ``crystal phase'' for z lying between z_c(M) and z_d(M). In
this phase, which is driven by entropy, particles, independent of species,
preferentially occupy one of the sublattices, i.e. spatial symmetry but not
particle symmetry is broken. The transition at z_d(M) appears to be first order
for M \geq 5 putting it in the Potts model universality class. For large M the
transition between the crystalline and demixed phase at z_d(M) can be proven to
be first order with z_d(M) \sim M-2 + 1/M + ..., while z_c(M) is argued to
behave as \mu_{cr}/M, with \mu_{cr} the value of the fugacity at which the one
component hard square lattice gas has a transition, and to be always of the
Ising type. Explicit calculations for the Bethe lattice with the coordination
number q=4 give results similar to those for the square lattice except that the
transition at z_d(M) becomes first order at M>2. This happens for all q,
consistent with the model being in the Potts universality class.Comment: 26 pages, 15 postscript figure
Magnetic order in the Ising model with parallel dynamics
It is discussed how the equilibrium properties of the Ising model are
described by an Hamiltonian with an antiferromagnetic low temperature behavior
if only an heat bath dynamics, with the characteristics of a Probabilistic
Cellular Automaton, is assumed to determine the temporal evolution of the
system.Comment: 9 pages, 3 figure
A Contour Method on Cayley tree
We consider a finite range lattice models on Cayley tree with two basic
properties: the existence of only a finite number of ground states and with
Peierls type condition. We define notion of a contour for the model on the
Cayley tree. By a contour argument we show the existence of different
(where is the number of ground states) Gibbs measures.Comment: 12 page
Consistent Anisotropic Repulsions for Simple Molecules
We extract atom-atom potentials from the effective spherical potentials that
suc cessfully model Hugoniot experiments on molecular fluids, e.g., and
. In the case of the resulting potentials compare very well with the
atom-atom potentials used in studies of solid-state propertie s, while for
they are considerably softer at short distances. Ground state (T=0K) and
room temperatu re calculations performed with the new potential resolve
the previous discrepancy between experimental and theoretical results.Comment: RevTeX, 5 figure
Generation of Primordial Cosmological Perturbations from Statistical Mechanical Models
The initial conditions describing seed fluctuations for the formation of
structure in standard cosmological models, i.e.the Harrison-Zeldovich
distribution, have very characteristic ``super-homogeneous'' properties: they
are statistically translation invariant, isotropic, and the variance of the
mass fluctuations in a region of volume V grows slower than V. We discuss the
geometrical construction of distributions of points in with similar
properties encountered in tiling and in statistical physics, e.g. the Gibbs
distribution of a one-component system of charged particles in a uniform
background (OCP). Modifications of the OCP can produce equilibrium correlations
of the kind assumed in the cosmological context. We then describe how such
systems can be used for the generation of initial conditions in gravitational
-body simulations.Comment: 7 pages, 3 figures, final version with minor modifications, to appear
in PR
Demagnetization via Nucleation of the Nonequilibrium Metastable Phase in a Model of Disorder
We study both analytically and numerically metastability and nucleation in a
two-dimensional nonequilibrium Ising ferromagnet. Canonical equilibrium is
dynamically impeded by a weak random perturbation which models homogeneous
disorder of undetermined source. We present a simple theoretical description,
in perfect agreement with Monte Carlo simulations, assuming that the decay of
the nonequilibrium metastable state is due, as in equilibrium, to the
competition between the surface and the bulk. This suggests one to accept a
nonequilibrium "free-energy" at a mesoscopic/cluster level, and it ensues a
nonequilibrium "surface tension" with some peculiar low-T behavior. We
illustrate the occurrence of intriguing nonequilibrium phenomena, including:
(i) Noise-enhanced stabilization of nonequilibrium metastable states; (ii)
reentrance of the limit of metastability under strong nonequilibrium
conditions; and (iii) resonant propagation of domain walls. The cooperative
behavior of our system may also be understood in terms of a Langevin equation
with additive and multiplicative noises. We also studied metastability in the
case of open boundaries as it may correspond to a magnetic nanoparticle. We
then observe burst-like relaxation at low T, triggered by the additional
surface randomness, with scale-free avalanches which closely resemble the type
of relaxation reported for many complex systems. We show that this results from
the superposition of many demagnetization events, each with a well- defined
scale which is determined by the curvature of the domain wall at which it
originates. This is an example of (apparent) scale invariance in a
nonequilibrium setting which is not to be associated with any familiar kind of
criticality.Comment: 26 pages, 22 figure
Effect of Composition Changes on the Structural Relaxation of a Binary Mixture
Within the mode-coupling theory for idealized glass transitions, we study the
evolution of structural relaxation in binary mixtures of hard spheres with size
ratios of the two components varying between 0.5 and 1.0. We find two
scenarios for the glassy dynamics. For small size disparity, the mixing yields
a slight extension of the glass regime. For larger size disparity, a
plasticization effect is obtained, leading to a stabilization of the liquid due
to mixing. For all , a decrease of the elastic moduli at the transition
due to mixing is predicted. A stiffening of the glass structure is found as is
reflected by the increase of the Debye-Waller factors at the transition points.
The critical amplitudes for density fluctuations at small and intermediate wave
vectors decrease upon mixing, and thus the universal formulas for the
relaxation near the plateau values describe a slowing down of the dynamics upon
mixing for the first step of the two-step relaxation scenario. The results
explain the qualitative features of mixing effects reported by Williams and van
Megen [Phys. Rev. E \textbf{64}, 041502 (2001)] for dynamical light-scattering
measurements on binary mixtures of hard-sphere-like colloids with size ratio
Role of chaos for the validity of statistical mechanics laws: diffusion and conduction
Several years after the pioneering work by Fermi Pasta and Ulam, fundamental
questions about the link between dynamical and statistical properties remain
still open in modern statistical mechanics. Particularly controversial is the
role of deterministic chaos for the validity and consistency of statistical
approaches. This contribution reexamines such a debated issue taking
inspiration from the problem of diffusion and heat conduction in deterministic
systems. Is microscopic chaos a necessary ingredient to observe such
macroscopic phenomena?Comment: Latex, 27 pages, 10 eps-figures. Proceedings of the Conference "FPU
50 years since" Rome 7-8 May 200
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