Critical properties of the one-dimensional forest-fire model

A. Honecker and I. Peschel

Physica A: Statistical Mechanics and its Applications, 1996, vol. 229, issue 3, 478-500

Abstract: A one-dimensional forest-fire model including lightnings is studied numerically and analytically. For the tree correlation function, a new correlation length with critical exponent v ≈ 56 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.

Date: 1996
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:229:y:1996:i:3:p:478-500

DOI: 10.1016/0378-4371(95)00441-6

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