No abstract

We study the criticality of a Potts interface by introducing a 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 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.

An exact renormalization group describes extremely slow, logarithmic diffusion in the presence of a biasing field on ramified fractal structures. Recursion equations are singular at the fixed point and the standard analysis to extract asymptotic behaviors has to be reconsidered. The model reproduces mechanisms working for biased diffusion on percolation clusters. For 1 ~d structures, logarithmic diffusions generalizing that discussed by Sinai [Theory Probab. Its Appl. 27, 256 (1982)] are obtained by the same methods.PACS numbers: 64.60. Ak, 71.55Jv Slow diffusion, with the average displacement R, growing in time t, as some power of lnf, has been exactly demonstrated by Sinai for a particle hopping on a onedimensional chain and subject at each site to an independent random bias [1]. There is numerical evidence that logarithmic diffusion could replace the anomalous power law one, in fractal structures, like the infinite incipient cluster (IIC) of percolation, when the diffusing particle is subject to the action of an external biasing field [2,3]. In this case the field is not random, but the structure of the fractal conspires with it and determines a localization effect, e.g., by pushing the particle towards dangling ends [4].Interestingly enough, the current understanding of such phenomena relies almost entirely on the picture of a particle diffusing in one dimension. This is the situation of the Sinai model, whose behavior is indeed easily understood once realized that, over a distance R along the chain, a potential barrier oc J~R develops by adding the local random biases with zero average. On the basis of Arrhenius law, overcoming such a barrier requires a time cce , from which R

PACS. 68.45Gd -Wetting. PACS. 05.70Fh -Phase transitions: general aspects. PACS. 82.65Dp -Thermodynamics of surfaces and interfaces.Abstract. -Transfer-matrix results in 2D show that wetting of a rough, self-affine wall induced by bulk bond disorder turns discontinuous as soon as the wall roughness exponent ζW exceeds ζ0 = 2/3, the spatial anisotropy index of interface fluctuations in the bulk. For ζW < 2/3 critical wetting is recovered, in the same universality class as for the flat-wall case. These and related findings suggest a free-energy structure such to imply first-order wetting also without disorder, or in 3D, whenever ζW exceeds the appropriate ζ0. The same thresholds should apply also with van der Waals forces, in cases when ζ0 implies a strong-fluctuation regime. . An example is offered by the 2D Ising model on semi-infinite lattice. At T = 0, with suitable boundary conditions, the interface can be localized on a line of weak ferromagnetic bonds along the edge (wall). If the bulk couplings are disordered, upon reducing wall attraction depinning eventually occurs. This ill-condensed matter version of critical wetting in 2D belongs to a different universality class as similar transitions controlled by thermal fluctuations alone. Indeed, the mean wall-interface distance h diverges as ∆ −ψ , where ψ = 2 [1] and ∆ measures the deviation from critical edge attraction conditions. ψ = 1 holds for the thermal case without disorder [6].An as yet unanswered question concerns the possible effect of additional, geometrical surface disorder on this type of wetting. Rough substrate walls with self-affine geometry, are produced in experiments [7], [8] and adsorption phenomena have been already observed on them [8]. On the other hand, interface depinning belongs to a more general class of disorder-induced delocalization phenomena of fluctuating manifolds from extended defects [9].