Phenomenological Free-Energy-Function, Fractal Dimension, and Critical Indices for Phase Transition Systems

Considering the relations between interaction terms in microscopic Hamiltonian and terms in macroscopic Landau's free-energy-function (FEF) of a phase transition system, we propose a modified Landau's phenomenological FEF to deal with critical phenomena. According to scaling symmetry, it is indeed true that, the dimension of interaction space is fractal at critical points for a phase transition system. Following these analyses, we obtain all the critical indices reasonably classified in the classes denoted by , which satisfy all the scaling laws and coincide with experiments. A cogent example is given.