Branching Interfaces with Infinitely Strong Couplings

A hierarchical froth model of the interface of a random $q$-state Potts ferromagnet in $2D$ is studied by recursive methods. A fraction $p$ of the nearest neighbour bonds is made inaccessible to domain walls by infinitely strong ferromagnetic couplings. Energetic and geometric scaling properties of the interface are controlled by zero temperature fixed distributions. For $p<p_c$, the directed percolation threshold, the interface behaves as for $p=0$, and scaling supports random Ising ($q=2$) critical behavior for all $q$'s. At $p=p_c$ three regimes are obtained for different ratios of ferro vs. antiferromagnetic couplings. With rates above a threshold value the interface is linear ( fractal dimension $d_f=1$) and its energy fluctuations, $\Delta E$ scale with length as $\Delta E\propto L^{\omega}$, with $\omega\simeq 0.48$. When the threshold is reached the interface branches at all scales and is fractal ($d_f\simeq 1.046$) with $\omega_c \simeq 0.51$. Thus, at $p_c$, dilution modifies both low temperature interfacial properties and critical scaling. Below threshold the interface becomes a probe of the backbone geometry (\df\simeq{\bar d}\simeq 1.305; $\bar d$ = backbone fractal dimension ), which even controls energy fluctuations ($\omega\simeq d_f\simeq\bar d$). Numerical determinations of directed percolation exponents on diamond hierarchical lattice are also presented.Comment: 16 pages, 3 Postscript figure

The Unusual Universality of Branching Interfaces in Random Media

We study the criticality of a Potts interface by introducing a {\it froth} model which, unlike its SOS Ising counterpart, incorporates bubbles of different phases. The interface is fractal at the phase transition of a pure system. However, a position space approximation suggests that the probability of loop formation vanishes marginally at a transition dominated by {\it strong random bond disorder}. This implies a linear critical interface, and provides a mechanism for the conjectured equivalence of critical random Potts and Ising models.Comment: REVTEX, 13 pages, 3 Postscript figures appended using uufile

First order wetting of rough substrates and quantum unbinding

Replica and functional renormalization group methods show that, with short range substrate forces or in strong fluctuation regimes, wetting of a self-affine rough wall in 2D turns first-order as soon as the wall roughness exponent exceeds the anisotropy index of bulk interface fluctuations. Different thresholds apply with long range forces in mean field regimes. For bond-disordered bulk, fixed point stability suggests similar results, which ultimately rely on basic properties of quantum bound states with asymptotically power-law repulsive potentials.Comment: 11 pages, 1 figur

Finite Size Scaling Analysis of Biased Diffusion on Fractals

Diffusion on a T fractal lattice under the influence of topological biasing fields is studied by finite size scaling methods. This allows to avoid proliferation and singularities which would arise in a renormalization group approach on infinite system as a consequence of logarithmic diffusion. Within the scheme, logarithmic diffusion is proved on the basis of an analysis of various temporal scales such as first passage time moments and survival probability characteristic time. This confirms and puts on firmer basis previous renormalization group results. A careful study of the asymptotic occupation probabilities of different kinds of lattice points allows to elucidate the mechanism of trapping into dangling ends, which is responsible of the logarithmic time dependence of average displacement.Comment: 17 pages TeX, 3 Postscript figure

Analysis of two cross-contamination cases of <i>Campylobacter jejuni</i> foodborne disease in fragile subjects in the territory of a Local Health Authority in Tuscany, Italy

Campylobacteriosis is the most reported foodborne disease in the European Union, with more than 100,000 confirmed cases annually. Human infection can be caused by a low infectious dose, and in fragile populations, the food disease can manifest itself in acute and severe forms. This study aims to analyze two cases of campylobacteriosis in fragile people caused by Campylobacter jejuni in 2023 in Tuscany and the actions of the Local Health Competent Authority. From the results of the related investigations, it was possible to attribute both cases of foodborne diseases to unsafe food management during preparation/administration. Given the peculiar characteristics of the etiological agent, it is necessary to focus the attention of the population, especially those who deal with fragile subjects, on the good hygiene practices to be followed both at home and in collective catering