We introduce a Renormalization scheme for the one- and two-dimensional Forest-Fire models in order to characterize the nature of the critical state and its scale invariant dynamics. We show the existence of a relevant scaling field associated with a repulsive fixed point. These models are therefore critical in the usual sense because the fixed point value of the control parameter is crucial in order to get criticality and it is not just the expression of a time scale separation. This general scheme allows us to calculate analytically the critical exponents for the one- and two-dimensional cases. The results obtained are in good agreement with exact or numerical results.
Renormalization group approach for forest-fire models / Loreto, Vittorio; Pietronero, Luciano; A., Vespignani; S., Zapperi. - In: FRACTALS-COMPLEX GEOMETRY PATTERNS AND SCALING IN NATURE AND SOCIETY. - ISSN 0218-348X. - STAMPA. - 3(3):(1995), pp. 445-452. (Intervento presentato al convegno Benoit Mandelbrot Festschrift tenutosi a CURACAO, NETH ANTILLES nel 2 Feb. 1995) [10.1142/S0218348X95000369].
Renormalization group approach for forest-fire models
LORETO, Vittorio;PIETRONERO, Luciano;
1995
Abstract
We introduce a Renormalization scheme for the one- and two-dimensional Forest-Fire models in order to characterize the nature of the critical state and its scale invariant dynamics. We show the existence of a relevant scaling field associated with a repulsive fixed point. These models are therefore critical in the usual sense because the fixed point value of the control parameter is crucial in order to get criticality and it is not just the expression of a time scale separation. This general scheme allows us to calculate analytically the critical exponents for the one- and two-dimensional cases. The results obtained are in good agreement with exact or numerical results.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
