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Critical properties of the one-dimensional forest-fire model

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  • Honecker, A.
  • Peschel, I.

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.

Suggested Citation

  • Honecker, A. & Peschel, I., 1996. "Critical properties of the one-dimensional forest-fire model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 229(3), pages 478-500.
    • Handle: RePEc:eee:phsmap:v:229:y:1996:i:3:p:478-500
    DOI: 10.1016/0378-4371(95)00441-6
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    1. Drossel, B. & Schwabl, F., 1992. "Self-organized criticality in a forest-fire model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 191(1), pages 47-50.
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    1. Honecker, A. & Peschel, I., 1997. "Length scales and power laws in the two-dimensional forest-fire model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 239(4), pages 509-530.

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