43,298 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
Collapse transition in polymer models with multiple monomers per site and multiple bonds per edge
We present results from extensive Monte Carlo simulations of polymer models
where each lattice site can be visited by up to monomers and no restriction
is imposed on the number of bonds on each lattice edge. These \textit{multiple
monomer per site} (MMS) models are investigated on the square and cubic
lattices, for and , by associating Boltzmann weights ,
and to sites visited by 1, 2 and
3 monomers, respectively. Two versions of the MMS models are considered for
which immediate reversals of the walks are allowed (RA) or forbidden (RF). In
contrast to previous simulations of these models, we find the same
thermodynamic behavior for both RA and RF versions. In three-dimensions, the
phase diagrams - in space - are featured by coil and
globule phases separated by a line of points, as thoroughly
demonstrated by the metric , crossover and entropic
exponents. The existence of the -lines is also confirmed by the second
virial coefficient. This shows that no discontinuous collapse transition exists
in these models, in contrast to previous claims based on a weak bimodality
observed in some distributions, which indeed exists in a narrow region very
close to the -line when . Interestingly, in
two-dimensions, only a crossover is found between the coil and globule phases
Width and extremal height distributions of fluctuating interfaces with window boundary conditions
We present a detailed study of squared local roughness (SLRDs) and local
extremal height distributions (LEHDs), calculated in windows of lateral size
, for interfaces in several universality classes, in substrate dimensions
and . We show that their cumulants follow a Family-Vicsek
type scaling, and, at early times, when ( is the correlation
length), the rescaled SLRDs are given by log-normal distributions, with their
th cumulant scaling as . This give rise to an
interesting temporal scaling for such cumulants , with . This scaling is analytically
proved for the Edwards-Wilkinson (EW) and Random Deposition interfaces, and
numerically confirmed for other classes. In general, it is featured by small
corrections and, thus, it yields exponents 's (and, consequently,
, and ) in nice agreement with their respective universality
class. Thus, it is an useful framework for numerical and experimental
investigations, where it is, usually, hard to estimate the dynamic and
mainly the (global) roughness exponents. The stationary (for ) SLRDs and LEHDs of Kardar-Parisi-Zhang (KPZ) class are also investigated
and, for some models, strong finite-size corrections are found. However, we
demonstrate that good evidences of their universality can be obtained through
successive extrapolations of their cumulant ratios for long times and large
's. We also show that SLRDs and LEHDs are the same for flat and curved KPZ
interfaces.Comment: 11 pages, 10 figures, 4 table
Roughness exponents and grain shapes
In surfaces with grainy features, the local roughness shows a crossover
at a characteristic length , with roughness exponent changing from
to a smaller . The grain shape, the choice of
or height-height correlation function (HHCF) , and the procedure to
calculate root mean-square averages are shown to have remarkable effects on
. With grains of pyramidal shape, can be as low as 0.71,
which is much lower than the previous prediction 0.85 for rounded grains. The
same crossover is observed in the HHCF, but with initial exponent
for flat grains, while for some conical grains it may
increase to . The universality class of the growth process
determines the exponents after the crossover, but has no
effect on the initial exponents and , supporting the
geometric interpretation of their values. For all grain shapes and different
definitions of surface roughness or HHCF, we still observe that the crossover
length is an accurate estimate of the grain size. The exponents obtained
in several recent experimental works on different materials are explained by
those models, with some surface images qualitatively similar to our model
films.Comment: 7 pages, 6 figures and 2 table
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