Large scale behavior of a two-dimensional model of anisotropic branched polymers.

We study critical properties of anisotropic branched polymers modeled by semi-directed lattice animals on a triangular lattice. Using the exact transfer-matrix approach on strips of quite large widths and phenomenological renormalization group analysis, we obtained pretty good estimates of various critical exponents in the whole high-temperature region, including the point of collapse transition. Our numerical results suggest that this collapse transition belongs to the universality class of directed percolation.

Density of zeros of the ferromagnetic Ising model on a family of fractals.

We studied distribution of zeros of the partition function of the ferromagnetic Ising model near the Yang-Lee edge on a family of Sierpinski gasket lattices whose members are labeled by an integer b (2 ≤ b<∞). The obtained exact results on the first seven members of this family show that, for b ≥ 4, associated correlation length diverges more slowly than any power law when distance δh from the edge tends to zero, ξ_{YL}∼exp[ln(b)sqrt[|ln(δh)|/ln(λ{0})]], λ{0} being a decreasing function of b. We suggest a possible scenario for the emergence of the usual power-law behavior in the limit of very large b when fractal lattices become almost compact.