46 research outputs found
Transfer-matrix study of a hard-square lattice gas with two kinds of particles and density anomaly
Using transfer matrix and finite-size scaling methods, we study the
thermodynamic behavior of a lattice gas with two kinds of particles on the
square lattice. Only excluded volume interactions are considered, so that the
model is athermal. Large particles exclude the site they occupy and its four
first neighbors, while small particles exclude only their site. Two
thermodynamic phases are found: a disordered phase where large particles occupy
both sublattices with the same probability and an ordered phase where one of
the two sublattices is preferentially occupied by them. The transition between
these phases is continuous at small concentrations of the small particles and
discontinuous at larger concentrations, both transitions are separated by a
tricritical point. Estimates of the central charge suggest that the critical
line is in the Ising universality class, while the tricritical point has
tricritical Ising (Blume-Emery-Griffiths) exponents. The isobaric curves of the
total density as functions of the fugacity of small or large particles display
a minimum in the disordered phase.Comment: 9 pages, 7 figures and 4 table
Nature of the collapse transition in interacting self-avoiding trails
We study the interacting self-avoiding trail (ISAT) model on a Bethe lattice
of general coordination and on a Husimi lattice built with squares and
coordination . The exact grand-canonical solutions of the model are
obtained, considering that up to monomers can be placed on a site and
associating a weight for a -fold visited site. Very rich phase
diagrams are found with non-polymerized (NP), regular polymerized (P) and dense
polymerized (DP) phases separated by lines (or surfaces) of continuous and
discontinuous transitions. For Bethe lattice with and , the collapse
transition is identified with a bicritical point and the collapsed phase is
associated to the dense polymerized phase (solid-like) instead of the regular
polymerized phase (liquid-like). A similar result is found for the Husimi
lattice, which may explain the difference between the collapse transition for
ISAT's and for interacting self-avoiding walks on the square lattice. For
and (studied on the Bethe lattice only), a more complex phase diagram is
found, with two critical planes and two coexistence surfaces, separated by two
tricritical and two critical end-point lines meeting at a multicritical point.
The mapping of the phase diagrams in the canonical ensemble is discussed and
compared with simulational results for regular lattices.Comment: 12 pages, 13 figure
Simple Model for Attraction between Like-Charged Polyions
We present a simple model for the possible mechanism of appearance of
attraction between like charged polyions inside a polyelectrolyte solution. The
attraction is found to be short ranged, and exists only in presence of
multivalent counterions. The attraction is produced by the correlations in the
condensed layers of counterions surrounding each polyion, and appears only if
the number of condensed counterions exceeds the threshold, ,
where is the valence of counterions and is the polyion charge.Comment: 4 pages, 4 eps figures, also available at
http://www.if.ufrgs.br/~arenzon Figure added and a more detailed discussion
of conclusion
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
The nature of attraction between like charged rods
Comment on the paper of Ha and Liu (Phys. Rev. Lett. {\bf 79}, 1289 (1997))
regarding the nature of attraction between like charged rods. We demostrate
that their results do not produce the correct low temperature limit.Comment: Comment to appear in Phys. Rev. Let
Polymers with attractive interactions on the Husimi tree
We obtain the solution of models of self-avoiding walks with attractive
interactions on Husimi lattices built with squares. Two attractive interactions
are considered: between monomers on first-neighbor sites and not consecutive
along a walk and between bonds located on opposite edges of elementary squares.
For coordination numbers q>4, two phases, one polymerized the other
non-polymerized, are present in the phase diagram. For small values of the
attractive interaction the transition between those phases is continuous, but
for higher values a first-order transition is found. Both regimes are separated
by a tricritical point. For q=4 a richer phase diagram is found, with an
additional (dense) polymerized phase, which is stable for for sufficiently
strong interactions between bonds. The phase diagram of the model in the
three-dimensional parameter space displays surfaces of continuous and
discontinuous phase transitions and lines of tricritical points, critical
endpoints and triple points.Comment: 7 pages, 6 figure