## 1997 |

Vespignani, Alessandro; Zapperi, Stefano; Loreto, Vittorio Dynamically driven renormalization group Journal Article JOURNAL OF STATISTICAL PHYSICS, 88 , pp. 47–79, 1997. Abstract | Links | BibTeX | Tags: DDRG, loreto, self_organization, statistical_physics, vespignani, zapperi @article{b, title = {Dynamically driven renormalization group}, author = {Alessandro Vespignani and Stefano Zapperi and Vittorio Loreto}, url = {http://www.springerlink.com/content/d1215122128712g1/, http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=A1997XT83300003&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=0c7ff228ccbaaa74236f48834a34396a}, year = {1997}, date = {1997-01-01}, journal = {JOURNAL OF STATISTICAL PHYSICS}, volume = {88}, pages = {47--79}, abstract = {We present a detailed discussion of a novel dynamical renormalization group scheme: the dynamically driven renormalization group (DDRG). This is a general renormalization method developed for dynamical systems with non-equilibrium critical steady state. The method is based on a real-space renormalization scheme driven by a dynamical steady-state condition which acts as a feedback on the transformation equations. This approach has been applied to open nonlinear systems such as self-organized critical phenomena, and it allows the analytical evaluation of scalling dimensions and critical exponents. Equilibrium models at the critical point can also be considered. The explicit application to some models and the corresponding results are discussed.}, keywords = {DDRG, loreto, self_organization, statistical_physics, vespignani, zapperi}, pubstate = {published}, tppubtype = {article} } We present a detailed discussion of a novel dynamical renormalization group scheme: the dynamically driven renormalization group (DDRG). This is a general renormalization method developed for dynamical systems with non-equilibrium critical steady state. The method is based on a real-space renormalization scheme driven by a dynamical steady-state condition which acts as a feedback on the transformation equations. This approach has been applied to open nonlinear systems such as self-organized critical phenomena, and it allows the analytical evaluation of scalling dimensions and critical exponents. Equilibrium models at the critical point can also be considered. The explicit application to some models and the corresponding results are discussed. |

## 1996 |

Hur, Asa Ben; Hallgass, Riccardo; Loreto, Vittorio A renormalization procedure for directed sandpile models Journal Article PHYSICAL REVIEW E, 54 , pp. 1426–1432, 1996. Abstract | Links | BibTeX | Tags: ben-hur, DDRG, hallgass, loreto, self_organization, statistical_physics @article{b, title = {A renormalization procedure for directed sandpile models}, author = {Asa Ben Hur and Riccardo Hallgass and Vittorio Loreto}, url = {http://pre.aps.org/abstract/PRE/v54/i2/p1426_1, http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=A1996VD67400057&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=0c7ff228ccbaaa74236f48834a34396a}, year = {1996}, date = {1996-01-01}, journal = {PHYSICAL REVIEW E}, volume = {54}, pages = {1426--1432}, publisher = {AMERICAN PHYSICAL SOC}, abstract = {Directed models of self-organized criticality are studied in the framework of a real-space renormalization group of a different type. The identification of a suitable phase space in which to define the renormalization transformation and the coupling with the stationarity condition enables us to clarify the nature of the critical state. The renormalization equations are found to have an attractive fixed point, as expected from the self-critical nature of the model. The values of the critical exponents obtained by this procedure are in excellent agreement with exact results.}, keywords = {ben-hur, DDRG, hallgass, loreto, self_organization, statistical_physics}, pubstate = {published}, tppubtype = {article} } Directed models of self-organized criticality are studied in the framework of a real-space renormalization group of a different type. The identification of a suitable phase space in which to define the renormalization transformation and the coupling with the stationarity condition enables us to clarify the nature of the critical state. The renormalization equations are found to have an attractive fixed point, as expected from the self-critical nature of the model. The values of the critical exponents obtained by this procedure are in excellent agreement with exact results. |

Vespignani, Alessandro; Zapperi, Stefano; Loreto, Vittorio Renormalization of non-equilibrium systems with critical stationary state Journal Article PHYSICAL REVIEW LETTERS, 77 , pp. 4560–4563, 1996. Abstract | Links | BibTeX | Tags: DDRG, loreto, self_organization, statistical_physics, vespignani, zapperi @article{b, title = {Renormalization of non-equilibrium systems with critical stationary state}, author = {Alessandro Vespignani and Stefano Zapperi and Vittorio Loreto}, url = {http://prl.aps.org/abstract/PRL/v77/i22/p4560_1 http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=A1996VU50200020&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=0c7ff228ccbaaa74236f48834a34396a}, year = {1996}, date = {1996-01-01}, journal = {PHYSICAL REVIEW LETTERS}, volume = {77}, pages = {4560--4563}, abstract = {We introduce the general formulation of a renormalization method suitable to study the critical properties of non-equilibrium systems with steady-states: the Dynamically Driven Renormalization Group. We renormalize the time evolution operator by computing the rescaled time transition rate between coarse grained states. The obtained renormalization equations are coupled to a stationarity condition which provides the approximate non-equilibrium statistical weights of steady-state configurations to be used in the calculations. In this way we are able to write recursion relations for the parameters evolution under scale change, from which we can extract numerical values for the critical exponents. This general framework allows the systematic analysis of several models showing self-organized criticality in terms of usual concepts of phase transitions and critical phenomena.}, keywords = {DDRG, loreto, self_organization, statistical_physics, vespignani, zapperi}, pubstate = {published}, tppubtype = {article} } We introduce the general formulation of a renormalization method suitable to study the critical properties of non-equilibrium systems with steady-states: the Dynamically Driven Renormalization Group. We renormalize the time evolution operator by computing the rescaled time transition rate between coarse grained states. The obtained renormalization equations are coupled to a stationarity condition which provides the approximate non-equilibrium statistical weights of steady-state configurations to be used in the calculations. In this way we are able to write recursion relations for the parameters evolution under scale change, from which we can extract numerical values for the critical exponents. This general framework allows the systematic analysis of several models showing self-organized criticality in terms of usual concepts of phase transitions and critical phenomena. |

Loreto, Vittorio; Vespignani, Alessandro; Zapperi, Stefano Renormalization scheme for forest-fire models Journal Article JOURNAL OF PHYSICS. A, MATHEMATICAL AND GENERAL, 29 , pp. 2981–3004, 1996. Links | BibTeX | Tags: DDRG, loreto, self_organization, statistical_physics, vespignani, zapperi @article{b, title = {Renormalization scheme for forest-fire models}, author = {Vittorio Loreto and Alessandro Vespignani and Stefano Zapperi}, url = {http://www.scopus.com/inward/record.url?eid=2-s2.0-0040108749&partnerID=65&md5=f34393a56c2dfc0797f394df2fda943a http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=A1996UU80300008&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=0c7ff228ccbaaa74236f48834a34396a}, year = {1996}, date = {1996-01-01}, journal = {JOURNAL OF PHYSICS. A, MATHEMATICAL AND GENERAL}, volume = {29}, pages = {2981--3004}, publisher = {IOP Publishing Limited:Dirac House, Temple Back, Bristol BS1 6BE United Kingdom:011 44 117 9297481, EMAIL: custserv@iop.org, INTERNET: http://www.iop.org, Fax: 011 44 117 9294318}, keywords = {DDRG, loreto, self_organization, statistical_physics, vespignani, zapperi}, pubstate = {published}, tppubtype = {article} } |

## 1995 |

Loreto, Vittorio; Pietronero, Luciano; Vespignani, Alessandro; Zapperi, Stefano Renormalization group approach to the crtical behavior of the forest-fire model Journal Article PHYSICAL REVIEW LETTERS, 75 , pp. 465–468, 1995. Abstract | Links | BibTeX | Tags: DDRG, loreto, pietronero, self_organization, statistical_physics, vespignani, zapperi @article{b, title = {Renormalization group approach to the crtical behavior of the forest-fire model}, author = {Vittorio Loreto and Luciano Pietronero and Alessandro Vespignani and Stefano Zapperi}, url = {http://prl.aps.org/abstract/PRL/v75/i3/p465_1, http://www.scopus.com/inward/record.url?eid=2-s2.0-0000977225&partnerID=65&md5=4f03991047dc2820ef6c00a2e81b3c7d http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=A1995RK33000028&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=0c7ff228ccbaaa74236f48834a34396a}, year = {1995}, date = {1995-01-01}, journal = {PHYSICAL REVIEW LETTERS}, volume = {75}, pages = {465--468}, abstract = {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 ν = 1.0, τ = 1.0 and ν = 0.65, τ = 1.16, respectively, for the one- and two-dimensional cases, in very good agreement with numerical simulations.}, keywords = {DDRG, loreto, pietronero, self_organization, statistical_physics, vespignani, zapperi}, pubstate = {published}, tppubtype = {article} } 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 ν = 1.0, τ = 1.0 and ν = 0.65, τ = 1.16, respectively, for the one- and two-dimensional cases, in very good agreement with numerical simulations. |

Other subjects