SCIPRESS FORMA
Forma, Vol. 4 (No. 1), pp. 59-64, 2001
Review

Kinetic Growth Percolation

Toshiya Ohtsuki

Department of Applied Physics, Fukui University, Fukui 910, Japan

(Received May 29, 1989; Accepted July 3, 1989)

Keywords: Percolation, Phase Transition, Fractal

Abstract. Nonequilibrium percolating-nonpercolating phase transitions found in kinetic growth processes are studied theoretically. It is shown that simple models belong to the same universality class as that of isotropic or directed percolation. A real-space renormalization group method and computer simulations are used to investigate generalized models. Phase diagrams are explicitly calculated and the nature of phase transitions is clarified. The influence of external fields is also argued. The appearance of a directed spreading phase and singular responses to external fields near a critical point are revealed.