CRITICAL PROPERTIES OF THE ONE-DIMENSIONAL FOREST-FIRE MODEL

A one-dimensional forest-fire model including lightnings is studied nu merically and analytically. For the tree correlation function, a new c orrelation length with critical exponent nu approximate to 5/6 is foun d by simulations. A Hamiltonian formulation is introduced which enable s one to study the stationary state close to the critical point using quantum-mechanical perturbation theory. With this formulation also the structure of the low-lying relaxation spectrum and the critical behav iour of the smallest complex gap are investigated numerically. Finally , it is shown that critical correlation functions can be obtained from a simplified model involving only the total number of trees although such simplified models are unable to reproduce the correct off-critica l behaviour.