Cluster analysis of the Ising model and universal finite-size scaling

The recent progress in the study of finite-size scaling (FSS) properties of the Ising model is briefly reviewed. We calculate the universal FSS functi ons for the Binder parameter g and the magnetization distribution function p(m) for the Ising model on L-1 x L-2 two-dimensional lattices with tilted boundary conditions. We show that the FSS functions are universal for fixed sets of the aspect ratio L-1/L-2 and the tilt parameter. We also study the percolating properties of the Ising model, giving attention to the effects of the aspect ratio of finite systems. We elucidate the origin of the comp lex structure of p(m) for the system with large aspect ratio by the multipl e-percolating-cluster argument. (C) 2000 Elsevier Science B.V. All rights r eserved.