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We study the phase diagram of fully directed lattice animals with nearest-neighbour interactions on the square lattice. This model comprises several interesting ensembles (directed site and bond trees, bond animals, strongly embeddable animals) as special cases and its collapse transition is equivalent to a directed bond percolation threshold. Precise estimates for the animal size exponents in the different phases and for the critical fugacities of these special ensembles are obtained from a phenomenological renormalization group analysis of the correlation lengths for strips of width up to n=17. The crossover region in the vicinity of the collapse transition is analyzed in detail and the crossover exponent $\phi$ is determined directly from the singular part of the free energy. We show using scaling arguments and an exact relation due to Dhar that $\phi$ is equal to the Fisher exponent $\sigma$ governing the size distribution of large directed percolation clusters., Comment: 23 pages, 3 figures; J. Phys. A 35 (2002) 2725

We studied oscillatory behavior of critical amplitudes for the Gaussian model on a hierarchical structure presented by a modified Sierpinski gasket lattice. This model is known to display non-standard critical behavior on the lattice under study. The leading singular behavior of the correlation length $\xi$ near the critical coupling $K=K_c$ is modulated by a function which is periodic in $\ln|\ln(K_c-K)|$. We have also shown that the common finite-size scaling hypothesis, according to which for a finite system at criticality $\xi$ should be of the order of the size of system, is not applicable in this case. As a consequence of this, the exact form of the leading singular behavior of $\xi$ differs from the one described earlier (which was based on the finite-size scaling assumption)., Comment: 9 pages (REVTEX), 2 figures (EPS), Phys. Rev. E (accepted)

We study the critical behavior of surface-interacting self-avoiding random walks on a class of truncated simplex lattices, which can be labeled by an integer $n\ge 3$. Using the exact renormalization group method we have been able to obtain the exact values of various critical exponents for all values of n up to n=6. We also derived simple formulas which describe the asymptotic behavior of these exponents in the limit of large n ($n\to\infty$). In spite of the fact that the coordination number of the lattice tends to infinity in this limit, we found that the most of the studied critical exponents approach certain finite values, which differ from corresponding values for simple random walks (without self-avoiding walk constraint)., Comment: 25 pages, Tex, 8 figures (eps)

The density of zeros of the partition function of the Ising model on a class of treelike lattices is studied. An exact closed-form expression for the pertinent critical exponents is derived by using a couple of recursion relations which have a singular behavior near the Yang-Lee edge., Comment: 9 pages AmsTex, 2 eps figures, to appear in J.Phys.A