Renormalization group approach to the critical behavior of the forest-fire model.

We introduce a renormalization scheme for the one- and two-dimensional forest-fire model 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. This model is therefore critical in the usual sense because the control parameter has to be tuned to its critical value in order to get criticality. It turns out that this is not just the condition for a time scale separation. The critical exponents are computed analytically and we obtain v = 1.0, T = 1.0 and v = 0.65, T = 1.16, respectively, for the one- and two-dimensional cases, in very good agreement with numerical simulations.

• Publication year

  1995

• Venue

  Physical Review Letters

• Publication date

  1995-05-25

• Fields of study

  Medicine, Physics

• Identifiers
  DOI 10.1103/physrevlett.75.465arXiv cond-mat/9505128PMID 10060028
• External record

  Open on Semantic Scholar

• Source metadata

  Semantic Scholar, PubMed

• No claims are published for this paper.

• No concepts are published for this paper.

• RENORMALIZATION SCHEME FOR FOREST-FIRE MODELS

  1996cited by this paper
• The fixed-scale transformation approach to fractal growth

  1995cited by this paper
• Renormalization approach to the self-organized critical behavior of sandpile models.

  1995cited by this paper
• Renormalization scheme for self-organized criticality in sandpile models.

  1994cited by this paper
• Scaling laws and simulation results for the self-organized critical forest-fire model.

  1994cited by this paper
• Self-organized critical forest-fire model: Mean-field theory and simulation results in 1 to 6 dimenisons.

  1993cited by this paper
• Exact results for the one-dimensional self-organized critical forest-fire model.

  1993cited by this paper
• Self-organized critical forest-fire model.

  1992cited by this paper
• Self-organized criticality.

  1988cited by this paper
• Self-organized criticality: An explanation of the 1/f noise.

  1987cited by this paper

• Forest fire as a temperature-pattern-driven depinning problem.

  2025cites this paper
• Phase transitions in in vivo or in vitro populations of spiking neurons belong to different universality classes

  2023cites this paper
• The emergence of scale-free fires in Australia

  2021cites this paper
• Is Deep Learning a Renormalization Group Flow?

  2020cites this paper
• Scale-Change Symmetry in the Rules Governing Neural Systems

  2019cites this paper
• Self-organised criticality via retro-synaptic signals in complex neural networks

  2016cites this paper
• An Introduction to Space Plasma Complexity

  2015cites this paper
• A Reaction-Diffusion Model of Cholinergic Retinal Waves

  2014cites this paper
• 25 Years of Self-Organized Criticality: Solar and Astrophysics

  2014cites this paper
• A Field Theory for Self-organised Criticality

  2013cites this paper
• A reaction-diffusion model of cholinergic retinal waves and self-organized criticality

  2013cites this paper
• TRANSIENTS IN A FOREST-FIRE SIMULATION MODEL WITH VARYING COMBUSTION NEIGHBOURHOODS AND WATERCOURSE FIREBREAKS

  2012cites this paper
• Power laws reveal phase transitions in landscape controls of fire regimes

  2012cites this paper
• A scale-invariant model for snow slab avalanches

  2009cites this paper
• Panarchy: Discontinuities Reveal Similarities in the Dynamic System Structure of Ecological and Social Systems

  2009cites this paper
• Wildland surface fire spread modelling, 1990–2007. 3: Simulation and mathematical analogue models

  2009cites this paper
• Universality in Self-Organized Criticality

  2008cites this paper
• Dynamics of the one-dimensional self-organized forest-fire model.

  2008cites this paper
• Universal scaling in wildfire fractal propagation

  2008cites this paper
• A review of wildland fire spread modelling, 1990-present 3: Mathematical analogues and simulation models

  2007cites this paper
• Background activity drives criticality of neuronal avalanches

  2007cites this paper
• Self-organized critical branching in systems that violate conservation laws

  2007cites this paper
• Time-series Analysis of Clusters in City Size Distributions

  2005cites this paper
• Assessing interaction networks with applications to catastrophe dynamics and disaster management

  2003cites this paper
• Complexity, Forced and/or Self-Organized Criticality, and Topological Phase Transitions in Space Plasmas

  2003cites this paper
• On modeling of geophysical problems

  2002cites this paper
• A scale invariant coupling of plants, water, energy, and terrain

  2002cites this paper
• A revised forest-fire cellular automaton for the nonlinear dynamics of the Earth’s magnetotail

  2001cites this paper
• Power law distributions of burst duration and interburst interval in the solar wind: turbulence or dissipative self-organized criticality?

  2000cites this paper
• Multiscale Assessment of Binary and Continuous Landcover Variables for MODIS Validation, Mapping, and Modeling Applications

  1999cites this paper
• ClaraT: Instructional Software for Fractal Pattern Generation and Analysis

  1999cites this paper
• Self-organized criticality in forest-fire models

  1999cites this paper
• Modified renormalization strategy for sandpile models.

  1999cites this paper
• DYNAMICALLY DRIVEN RENORMALIZATION GROUP APPLIED TO SELF-ORGANIZED CRITICAL SYSTEMS

  1998cites this paper
• Dynamical real space renormalization group applied to sandpile models.

  1998cites this paper
• Forest-fire as a model for the dynamics of disease epidemics

  1998cites this paper
• Motivation and Benefits of Complex Systems Approaches in Ecology

  1998cites this paper
• NOVEL POSITION-SPACE RENORMALIZATION GROUP FOR BOND DIRECTED PERCOLATION IN TWO DIMENSIONS

  1998cites this paper
• On the critical behaviour of simple epidemics

  1997cites this paper
• Dynamically driven renormalization group

  1996cites this paper
• Renormalization of Nonequilibrium Systems with Critical Stationary States.

  1996cites this paper
• Self-organized branching processes: Avalanche models with dissipation.

  1996cites this paper
• RENORMALIZATION GROUP STUDY OF SANDPILE ON THE TRIANGULAR LATTICE

  1996cites this paper
• Forest fires and other examples of self-organized criticality

  1996cites this paper
• RENORMALIZATION SCHEME FOR FOREST-FIRE MODELS

  1996cites this paper
• Critical behavior of the sandpile model as a self-organized branching process.

  1996cites this paper
• The Introduced Hawaiian Avifauna Reconsidered: Evidence for Self-Organized Criticality?

  1996cites this paper
• A scaling analysis of measles epidemics in a small population.

  1996cites this paper
• Word processors with line wrap: Cascading, self-organized criticality, random walks, diffusion, and predictability.

  1995cites this paper
• Critical properties of the one-dimensional forest-fire model

  1995cites this paper