TY - JOUR

T1 - Quantum field theory renormalization group approach to self-organized critical models

T2 - The case of random boundaries

AU - Volchenkov, D.

AU - Blanchard, P. H.

AU - Cessac, B.

N1 - Funding Information:
This work has been performed in connection with the international research project \The Sciences of Complexity: From Mathematics to technology to a Sustainable World", Zentrum für Interdisziplinäre Forschung (ZIF), Universität Bielefeld (Germany). One of the authors (D.V.) acknowledges the nancial support from the Alexander von Humboldt Foundation (Germany). D.V. and B.C. also acknowledge the nancial support from the Zentrum für Interdisziplinäre Forschung (ZIF), Universität Bielefeld.

PY - 2002/3/30

Y1 - 2002/3/30

N2 - The long time and large scale asymptotic behavior for a stochastic problem related to self-organized critical (SOC) models is studied in the framework of advanced quantum field theory renormalization group (RG) method. The threshold condition and time scale separation between the slow dynamics of energy injection and the fast dynamics of avalanches (relaxation) are taken into account in the model. Herewith, the reciprocal correlation time at wavenumber k scales as tc(k) α k-2+2η with some phenomenological parameter η > 0 corresponding to the anomalous diffusion coefficient z = 2(1 - η). The quantum field theory corresponding to the nonlinear stochastic problem is multi-plicatively renormalizable and has an infinite number of coupling constants. The RG equations have a two-dimensional manifold of fixed points. Some of them relate to the stable asymptotic solutions and stipulate a general scaling with the critical dimensions of time Δ[t] = -2 + 2η and the energy field Δ[E] = d/2 - 3(1 - η). Possible corrections to the leading asymptotic behavior are discussed.

AB - The long time and large scale asymptotic behavior for a stochastic problem related to self-organized critical (SOC) models is studied in the framework of advanced quantum field theory renormalization group (RG) method. The threshold condition and time scale separation between the slow dynamics of energy injection and the fast dynamics of avalanches (relaxation) are taken into account in the model. Herewith, the reciprocal correlation time at wavenumber k scales as tc(k) α k-2+2η with some phenomenological parameter η > 0 corresponding to the anomalous diffusion coefficient z = 2(1 - η). The quantum field theory corresponding to the nonlinear stochastic problem is multi-plicatively renormalizable and has an infinite number of coupling constants. The RG equations have a two-dimensional manifold of fixed points. Some of them relate to the stable asymptotic solutions and stipulate a general scaling with the critical dimensions of time Δ[t] = -2 + 2η and the energy field Δ[E] = d/2 - 3(1 - η). Possible corrections to the leading asymptotic behavior are discussed.

KW - Quantum field renormalization group

KW - Self-organized criticality

UR - http://www.scopus.com/inward/record.url?scp=0037197144&partnerID=8YFLogxK

U2 - 10.1142/S0217979202010130

DO - 10.1142/S0217979202010130

M3 - Article

AN - SCOPUS:0037197144

VL - 16

SP - 1171

EP - 1204

JO - International Journal of Modern Physics B

JF - International Journal of Modern Physics B

SN - 0217-9792

IS - 8

ER -