176 research outputs found
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 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 is derived from a hierarchical random deposition
process previously studied in statistical physics. Two biologically relevant
parameters, the probabilities of birth, , and of death, , determine the
carrying capacity . Due to the randomness the population depends strongly on
position, , and there is a distribution of carrying capacities, .
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 and . 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 . This leads to
an increase of the critical field and to a surface critical
temperature in zero field, , which exceeds the bulk . When the
sample is {\em mesoscopic} of linear size the surface induces
superconductivity in the interior for .
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, , goes to zero, using analytic
calculations. While standard finite-size scaling holds for the transition in
non-zero magnetic field , an anomalous critical-point shift is found for
H=0. The increase of 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 ,
characterized by a shift inversely proportional to the
radius .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
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