Apparent first-order wetting and anomalous scaling in the two-dimensional Ising model

The global phase diagram of wetting in the two-dimensional (2d) Ising model is obtained through exact calculation of the surface excess free energy. Besides a surface field for inducing wetting, a surface-coupling enhancement is included. The wetting transition is critical (second order) for any finite ratio of surface coupling J_s to bulk coupling J, and turns first order in the limit J_s/J to infinity. However, for J_s/J much larger than 1 the critical region is exponentially small and practically invisible to numerical studies. A distinct pre-asymptotic regime exists in which the transition displays first-order character. Surprisingly, in this regime the surface susceptibility and surface specific heat develop a divergence and show anomalous scaling with an exponent equal to 3/2.Comment: This new version presents the exact solution and its properties whereas the older version was based on an approximate numerical study of the mode

Majority-vote on undirected Barabasi-Albert networks

On Barabasi-Albert networks with z neighbours selected by each added site, the Ising model was seen to show a spontaneous magnetisation. This spontaneous magnetisation was found below a critical temperature which increases logarithmically with system size. On these networks the majority-vote model with noise is now studied through Monte Carlo simulations. However, in this model, the order-disorder phase transition of the order parameter is well defined in this system and this wasn't found to increase logarithmically with system size. We calculate the value of the critical noise parameter q_c for several values of connectivity $z$ of the undirected Barabasi-Albert network. The critical exponentes beta/nu, gamma/nu and 1/nu were calculated for several values of z.Comment: 15 pages with numerous figure

Hierarchical population model with a carrying capacity distribution

A time- and space-discrete model for the growth of a rapidly saturating local biological population $N(x,t)$ is derived from a hierarchical random deposition process previously studied in statistical physics. Two biologically relevant parameters, the probabilities of birth, $B$, and of death, $D$, determine the carrying capacity $K$. Due to the randomness the population depends strongly on position, $x$, and there is a distribution of carrying capacities, $\Pi (K)$. This distribution has self-similar character owing to the imposed hierarchy. The most probable carrying capacity and its probability are studied as a function of $B$ and $D$. The effective growth rate decreases with time, roughly as in a Verhulst process. The model is possibly applicable, for example, to bacteria forming a "towering pillar" biofilm. The bacteria divide on randomly distributed nutrient-rich regions and are exposed to random local bactericidal agent (antibiotic spray). A gradual overall temperature change away from optimal growth conditions, for instance, reduces bacterial reproduction, while biofilm development degrades antimicrobial susceptibility, causing stagnation into a stationary state.Comment: 25 pages, 11 (9+2) figure

Effects of confinement and surface enhancement on superconductivity

Within the Ginzburg-Landau approach a theoretical study is performed of the effects of confinement on the transition to superconductivity for type-I and type-II materials with surface enhancement. The superconducting order parameter is characterized by a negative surface extrapolation length $b$. This leads to an increase of the critical field $H_{c3}$ and to a surface critical temperature in zero field, $T_{cs}$, which exceeds the bulk $T_c$. When the sample is {\em mesoscopic} of linear size $L$ the surface induces superconductivity in the interior for $T T_{cs}$. In analogy with adsorbed fluids, superconductivity in thin films of type-I materials is akin to {\em capillary condensation} and competes with the interface delocalization or "wetting" transition. The finite-size scaling properties of capillary condensation in superconductors are scrutinized in the limit that the ratio of magnetic penetration depth to superconducting coherence length, $\kappa \equiv \lambda/\xi$, goes to zero, using analytic calculations. While standard finite-size scaling holds for the transition in non-zero magnetic field $H$, an anomalous critical-point shift is found for H=0. The increase of $T_c$ for H=0 is calculated for mesoscopic films, cylindrical wires, and spherical grains of type-I and type-II materials. Surface curvature is shown to induce a significant increase of $T_c$, characterized by a shift $T_c(R)-T_c(\infty)$ inversely proportional to the radius $R$.Comment: 37 pages, 5 figures, accepted for PR

Examination of the Necessity of Complete Wetting near Critical Points in Systems with Long-Range Forces

Cahn’s general argument for complete wetting in the vicinity of critical points is critically reviewed. Critical-point wetting does occur in systems with short-range (exponentially decaying) forces. Whenever short-range forces favor wetting, while at the same time there is a tendency towards drying due to weak long-range (algebraically decaying) forces, neither critical-point wetting nor drying takes place. In this case the thickness of the partial wetting layer diverges as the bulk correlation length upon approach of the critical point