BOUNDARY-CONDITIONS, LATTICE SHAPES, AND SCALING FUNCTIONS OF PHASE-TRANSITION MODELS

In this paper we briefly review our finding about the effects of bound ary conditions and lattice shapes on scaling functions in critical phe nomena. We present new examples to show that different boundary condit ions and lattice shapes may give quite different scaling functions for lattice phase transition models, but they give consistent critical po int, critical exponents, and thermodynamic order parameter from renorm alization group calculations. We also review our recent results about the universal scaling functions for bond and site percolations on plan ar lattices with different boundary conditions and lattice shapes.