Critical Properties of the One-Dimensional Forest-Fire Model

Abstract

The one-dimensional forest-fire model including lightnings is studied numerically and analytically. For the tree correlation function, a new correlation length with critical exponent ν~ 5/6 is found by simulations. A Hamiltonian formulation is introduced which enables 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 behaviour 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-critical behaviour.

24 pages (plain TeX), 4 PostScript figures, uses psfig.sty

References in corpus (7)

• Reaction-Diffusion Processes, Critical Dynamics and Quantum Chains
• Scaling laws and simulation results for the self--organized critical forest--fire model
• Exact Results for the One-Dimensional Self-Organized Critical Forest-Fire Model
• Renormalization group approach to the critical behavior of the forest fire model
• Criticality in Simple Models of Evolution
• Self-organized critical and synchronized states in a nonequilibrium percolation model
• Universality in the One-Dimensional Self-Organized Critical Forest-Fire Model

Cited by in corpus (4)

• Length Scales and Power Laws in the Two-Dimensional Forest-Fire Model
• Phase Transition in a Stochastic Forest Fire Model and Effects of the Definition of Neighbourhood
• One-dimensional general forest fire processes
• System-size independence of a large deviation function for frequency of events in a one-dimensional forest-fire model with a single ignition site