Abstract
The universality of critical exponents in critical phenomena has been well known for long time and it is generally believed that systems within a given universality class have different finite-size scaling functions. In 1984, Privman and Fisher proposed the idea of universal finite-size scaling functions (UFSSF) and nonuniversal metric factors for static critical phenomena. From 1984 to 1994, the progress of research in this direction was very slow. In this paper, we review recent developments relating to universal finite-size scaling functions in static and dynamic critical phenomena. The topics under discussion include: 1. UFSSF of the existence probability E p and the percolation probability P in lattice percolation models, 2. UFSSF of the probability for the appearance of n percolating clusters W n in lattice percolation models, 3. UFSSF of E p and W n in continuum percolation models, and 4. UFSSF in dynamic critical phenomena of the Ising model.
Published Version
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