The field theory approach to percolation processes

dc.contributor.authorJanssen, H. K.en
dc.contributor.authorTäuber, Uwe C.en
dc.contributor.departmentPhysicsen
dc.date.accessioned2016-09-30T13:10:39Zen
dc.date.available2016-09-30T13:10:39Zen
dc.date.issued2005-01-01en
dc.description.abstractWe review the field theory approach to percolation processes. Specifically, we focus on the so-called simple and general epidemic processes that display continuous nonequilibrium active to absorbing state phase transitions whose asymptotic features are governed respectively by the directed (DP) and dynamic isotropic percolation (dIP) universality classes. We discuss the construction of a field theory representation for these Markovian stochastic processes based on fundamental phenomenological considerations, as well as from a specific microscopic reaction-diffusion model realization. Subsequently we explain how dynamic renormalization group (RG) methods can be applied to obtain the universal properties near the critical point in an expansion about the upper critical dimensions d<sub>c</sub> = 4 (DP) and 6 (dIP). We provide a detailed overview of results for critical exponents, scaling functions, crossover phenomena, finite-size scaling, and also briefly comment on the influence of long-range spreading, the presence of a boundary, multispecies generalizations, coupling of the order parameter to other conserved modes, and quenched disorder.en
dc.description.versionPublished versionen
dc.format.extent147 - 192 (46) page(s)en
dc.format.mimetypeapplication/pdfen
dc.identifier.doihttps://doi.org/10.1016/j.aop.2004.09.011en
dc.identifier.issn0003-4916en
dc.identifier.issue1en
dc.identifier.urihttp://hdl.handle.net/10919/73113en
dc.identifier.volume315en
dc.language.isoenen
dc.publisherAcademic Press – Elsevieren
dc.relation.urihttp://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000226780300006&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=930d57c9ac61a043676db62af60056c1en
dc.rightsIn Copyrighten
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/en
dc.subjectPhysics, Multidisciplinaryen
dc.subjectPhysicsen
dc.subjectpercolationen
dc.subjectepidemic processesen
dc.subjectdirected percolationen
dc.subjectdynamic isotropic percolationen
dc.subjectactive to absorbing phase transitionsen
dc.subjectrenormalization group theoryen
dc.subjectdynamic critical phenomenaen
dc.subjectcrossoveren
dc.subjectSTOCHASTIC-EVOLUTION PROCESSESen
dc.subjectUNIVERSAL SCALING BEHAVIORen
dc.subjectPAIR-CONTACT PROCESSen
dc.subjectORDER EPSILON-TERMSen
dc.subjectDIRECTED PERCOLATIONen
dc.subjectRENORMALIZATION-GROUPen
dc.subjectPHASE-TRANSITIONSen
dc.subjectDYNAMICAL PERCOLATIONen
dc.subjectCELLULAR AUTOMATAen
dc.subjectABSORBING STATESen
dc.titleThe field theory approach to percolation processesen
dc.title.serialAnnals of Physicsen
dc.typeArticle - Refereeden
dc.type.dcmitypeTexten
pubs.organisational-group/Virginia Techen
pubs.organisational-group/Virginia Tech/All T&R Facultyen
pubs.organisational-group/Virginia Tech/Scienceen
pubs.organisational-group/Virginia Tech/Science/COS T&R Facultyen
pubs.organisational-group/Virginia Tech/Science/Physicsen

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