41 research outputs found
Phase diagram of a bidispersed hard rod lattice gas in two dimensions
We obtain, using extensive Monte Carlo simulations, virial expansion and a
high-density perturbation expansion about the fully packed monodispersed phase,
the phase diagram of a system of bidispersed hard rods on a square lattice. We
show numerically that when the length of the longer rods is , two continuous
transitions may exist as the density of the longer rods in increased, keeping
the density of shorter rods fixed: first from a low-density isotropic phase to
a nematic phase, and second from the nematic to a high-density isotropic phase.
The difference between the critical densities of the two transitions decreases
to zero at a critical density of the shorter rods such that the fully packed
phase is disordered for any composition. When both the rod lengths are larger
than , we observe the existence of two transitions along the fully packed
line as the composition is varied. Low-density virial expansion, truncated at
second virial coefficient, reproduces features of the first transition. By
developing a high-density perturbation expansion, we show that when one of the
rods is long enough, there will be at least two isotropic-nematic transitions
along the fully packed line as the composition is varied.Comment: 7 pages, 4 figure
Bethe approximation for a system of hard rigid rods: the random locally tree-like layered lattice
We study the Bethe approximation for a system of long rigid rods of fixed
length k, with only excluded volume interaction. For large enough k, this
system undergoes an isotropic-nematic phase transition as a function of density
of the rods. The Bethe lattice, which is conventionally used to derive the
self-consistent equations in the Bethe approximation, is not suitable for
studying the hard-rods system, as it does not allow a dense packing of rods. We
define a new lattice, called the random locally tree-like layered lattice,
which allows a dense packing of rods, and for which the approximation is exact.
We find that for a 4-coordinated lattice, k-mers with k>=4 undergo a continuous
phase transition. For even coordination number q>=6, the transition exists only
for k >= k_{min}(q), and is first order.Comment: 10 pages, 10 figure
Self-avoiding walks on a bilayer Bethe lattice
Artículo finalmente publicado en: Journal of Statistical Mechanics: Theory and Experiment; 2014; 4-2014; 1-16We propose and study a model of polymer chains in a bilayer. Each chain is confined in one of
the layers and polymer bonds on first neighbor edges in different layers interact. We also define and
comment results for a model with interactions between monomers on first neighbor sites of different
layers. The thermodynamic properties of the model are studied in the grand-canonical formalism
and both layers are considered to be Cayley trees. In the core region of the trees, which we may call
a bilayer Bethe lattice, we find a very rich phase diagram in the parameter space defined by the two
activities of monomers and the Boltzmann factor associated to the interlayer interaction between
bonds or monomers. Beside critical and coexistence surfaces, there are tricritical, bicritical and
critical endpoint lines, as well as higher order multicritical points.http://iopscience.iop.org/1742-5468/2014/4/P04002/articlesubmittedVersionFil: Serra, Pablo. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentina.Fil: Serra, Pablo. Consejo Nacional de Investigaciones Científicas y Técnicas. Instituto de Física Enrique Gaviola; Argentina.Fil: Serra, Pablo. Universidad Nacional de Córdoba. Instituto de Física Enrique Gaviola; Argentina.Fil: Stilck, Jürgen F. Universidade Federal Fluminense. Instituto de Física; Brazil.Fil: Stilck, Jürgen F. Institute of Science and Technology for Complex Systems; Brazil.Física de los Materiales Condensado
Solution on the Bethe lattice of a hard core athermal gas with two kinds of particles
Athermal lattice gases of particles with first neighbor exclusion have been
studied for a long time as simple models exhibiting a fluid-solid transition.
At low concentration the particles occupy randomly both sublattices, but as the
concentration is increased one of the sublattices is occupied preferentially.
Here we study a mixed lattice gas with excluded volume interactions only in the
grand-canonical formalism with two kinds of particles: small ones, which occupy
a single lattice site and large ones, which occupy one site and its first
neighbors. We solve the model on a Bethe lattice of arbitrary coordination
number . In the parameter space defined by the activities of both particles.
At low values of the activity of small particles () we find a continuous
transition from the fluid to the solid phase as the activity of large particles
() is increased. At higher values of the transition becomes
discontinuous, both regimes are separated by a tricritical point. The critical
line has a negative slope at and displays a minimum before reaching the
tricritical point, so that a reentrant behavior is observed for constant values
of in the region of low density of small particles. The isobaric curves
of the total density of particles as a function of (or ) show a
minimum in the fluid phase.Comment: 18 pages, 5 figures, 1 tabl
Entropy of polydisperse chains: solution on the Bethe lattice
We consider the entropy of polydisperse chains placed on a lattice. In
particular, we study a model for equilibrium polymerization, where the
polydispersivity is determined by two activities, for internal and endpoint
monomers of a chain. We solve the problem exactly on a Bethe lattice with
arbitrary coordination number, obtaining an expression for the entropy as a
function of the density of monomers and mean molecular weight of the chains. We
compare this entropy with the one for the monodisperse case, and find that the
excess of entropy due to polydispersivity is identical to the one obtained for
the one-dimensional case. Finally, we obtain an exponential distribution of
molecular weights.Comment: 5 pages, 2 figures. Reference place
Semi-flexible trimers on the square lattice in the full lattice limit
Trimers are chains formed by two lattice edges, and therefore three monomers.
We consider trimers placed on the square lattice, the edges belonging to the
same trimer are either colinear, forming a straight rod with unitary
statistical weight, or perpendicular, a statistical weight being
associated to these angular trimers. The thermodynamic properties of this model
are studied in the full lattice limit, where all lattice sites are occupied by
monomers belonging to trimers. In particular, we use transfer matrix techniques
to estimate the entropy of the system as a function of . The entropy
is a maximum at and our results are compared to earlier
studies in the literature for straight trimers (), angular trimers
() and for mixtures of equiprobable straight and angular
trimers ().Comment: 6 pages, 4 figure
Particle-wall collision statistics in the open circular billiard
In the open circular billiard particles are placed initially with a uniform
distribution in their positions inside a planar circular vesicle. They all have
velocities of the same magnitude, whose initial directions are also uniformly
distributed. No particle-particle interactions are included, only specular
elastic collisions of the particles with the wall of the vesicle. The particles
may escape through an aperture with an angle . The collisions of the
particles with the wall are characterized by the angular position and the angle
of incidence. We study the evolution of the system considering the probability
distributions of these variables at successive times the particle reaches
the border of the vesicle. These distributions are calculated analytically and
measured in numerical simulations. For finite apertures , a
particular set of initial conditions exists for which the particles are in
periodic orbits and never escape the vesicle. This set is of zero measure, but
the selection of angular momenta close to these orbits is observed after some
collisions, and thus the distributions of probability have a structure formed
by peaks. We calculate the marginal distributions up to , but for
a solution is found for arbitrary . The escape probability as
a function of decays with an exponent 4 for and
evidences for a power law decay are found for lower apertures as well.Comment: 11 pages, 14 figures. Typos corrected and two new figures added,
figure captions changed and additional discussions added. Version accepted
for publication in Physica
Solution of an associating lattice gas model with density anomaly on a Husimi lattice
We study a model of a lattice gas with orientational degrees of freedom which
resemble the formation of hydrogen bonds between the molecules. In this model,
which is the simplified version of the Henriques-Barbosa model, no distinction
is made between donors and acceptors in the bonding arms. We solve the model in
the grand-canonical ensemble on a Husimi lattice built with hexagonal
plaquettes with a central site. The ground-state of the model, which was
originally defined on the triangular lattice, is exactly reproduced by the
solution on this Husimi lattice. In the phase diagram, one gas and two liquid
(high density-HDL and low density-LDL) phases are present. All phase
transitions (GAS-LDL, GAS-HDL, and LDL-HDL) are discontinuous, and the three
phases coexist at a triple point. A line of temperatures of maximum density
(TMD) in the isobars is found in the metastable GAS phase, as well as another
line of temperatures of minimum density (TmD) appears in the LDL phase, part of
it in the stable region and another in the metastable region of this phase.
These findings are at variance with simulational results for the same model on
the triangular lattice, which suggested a phase diagram with two critical
points. However, our results show very good quantitative agreement with the
simulations, both for the coexistence loci and the densities of particles and
of hydrogen bonds. We discuss the comparison of the simulations with our
results.Comment: 12 pages, 5 figure