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 $K$ 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 $K=2$ and $K=3$, by associating Boltzmann weights $\omega_0=1$, $\omega_1=e^{\beta_1}$ and $\omega_2=e^{\beta_2}$ 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 $\beta_2 \times \beta_1$ - are featured by coil and globule phases separated by a line of $\Theta$ points, as thoroughly demonstrated by the metric $\nu_t$, crossover $\phi_t$ and entropic $\gamma_t$ exponents. The existence of the $\Theta$-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 $\Theta$-line when $\beta_1 < 0$. Interestingly, in two-dimensions, only a crossover is found between the coil and globule phases

Glass-ionomer Adhesives in Orthodontics: Clinical Implications and Future Research Directions

During the past ten years significant advances have been made in the development of glass-ionomer bonding adhesives. The beneficial effects of fluoride are well documented and an agent which reduces or prevents a white spot lesion that commonly occurs clinically, is desirable. There has been a notable lack of randomized clinical trials to determine the prevalence of white spot lesions after orthodontic treatment although it is often reported in the literature. White spot lesions pose health and esthetic problems and their proper clinical management has yet to be resolved. The objective of this paper Is to review the literature in this area and suggest a rationale for a clinical trial to assess the efficiency of glass-ionomer adhesives in facing the problem of decalcification and study the bond strength of these materials

The collision of two-kinks defects

We have investigated the head-on collision of a two-kink and a two-antikink pair that arises as a generalization of the $\phi^4$ model. We have evolved numerically the Klein-Gordon equation with a new spectral algorithm whose accuracy and convergence were attested by the numerical tests. As a general result, the two-kink pair is annihilated radiating away most of the scalar field. It is possible the production of oscillons-like configurations after the collision that bounce and coalesce to form a small amplitude oscillon at the origin. The new feature is the formation of a sequence of quasi-stationary structures that we have identified as lump-like solutions of non-topological nature. The amount of time these structures survives depends on the fine-tuning of the impact velocity.Comment: 14 pages, 9 figure

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 $l$, for interfaces in several universality classes, in substrate dimensions $d_s = 1$ and $d_s = 2$. We show that their cumulants follow a Family-Vicsek type scaling, and, at early times, when $\xi \ll l$ ($\xi$ is the correlation length), the rescaled SLRDs are given by log-normal distributions, with their $n$th cumulant scaling as $(\xi/l)^{(n-1)d_s}$. This give rise to an interesting temporal scaling for such cumulants $\left\langle w_n \right\rangle_c \sim t^{\gamma_n}$, with $\gamma_n = 2 n \beta + {(n-1)d_s}/{z} = \left[ 2 n + {(n-1)d_s}/{\alpha} \right] \beta$. 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 $\gamma_n$'s (and, consequently, $\alpha$, $\beta$ and $z$) 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 $z$ and mainly the (global) roughness $\alpha$ exponents. The stationary (for $\xi \gg l$) 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 $l$'s. We also show that SLRDs and LEHDs are the same for flat and curved KPZ interfaces.Comment: 11 pages, 10 figures, 4 table