Critical Properties of the One-Dimensional Forest-Fire Model

Details Critical Properties of the One-Dimensional Forest-Fire Model Critical Properties of the One-Dimensional Forest-Fire Model

1995-11-28

arxiv.org/abs/cond-mat/9511132v1

Physica A229 (1996) 478-500

Physics

Condensed Matter

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

Scientific paper

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 \nu ~ 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.

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