Branching interfaces with infinitely strong couplings

A hierarchical froth model of the interface of a random q-state Pens 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 behaviour for all q's. At p = p(c) three regimes are obtained for different rates of ferro versus 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 proportional to L(omega), with omega similar or equal to 0.48. When the threshold is reached the interface branches at all scales and is fractal (d(f) similar or equal to 1.046) with omega(c) similar or equal to 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 (d(f) similar or equal to (d) over bar similar or equal to 1.305; (d) over bar = backbone fractal dimension), which even controls energy fluctuations (omega similar or equal to d(f) similar or equal to (d) over bar). Numerical determinations of directed percolation exponents on diamond hierarchical lattice are also presented.