The recent progress in the study of finite-size scaling (FSS) properties of the Ising model is briefly reviewed. We calculate the universal FSS functions for the Binder parameter g and the magnetization distribution function p(m) for the Ising model on L1×L2 two-dimensional lattices with tilted...

We briefly review recent work on universal finite-size scaling functions (UFSSFs) and quantities in percolation models. The topics under discussion include: (a) UFSSFs for the existence probability (also called crossing probability) Ep, the percolation probability P, and the probability Wn of...

We derive quenched subdiffusive lower bounds for the exit time τ(n) from a box of size n for the simple random walk on the planar invasion percolation cluster. The first part of the paper is devoted to proving an almost sure analogue of H. Kesten’s subdiffusivity theorem for the random walk...