Two-Loop Renormalization-Group Analysis of the Burgers-Kardar-Parisi-Zhang Equation
| dc.contributor.author | Frey, E. | en |
| dc.contributor.author | Täuber, Uwe C. | en |
| dc.contributor.department | Physics | en |
| dc.date.accessioned | 2016-09-30T00:18:59Z | en |
| dc.date.available | 2016-09-30T00:18:59Z | en |
| dc.date.issued | 1994-08 | en |
| dc.description.abstract | A systematic analysis of the Burgers—Kardar–Parisi–Zhang equation in d+ 1 dimensions by dynamic renormalization group theory is described. The fixed points and exponents are calculated to two–loop order. We use the dimensional regularization scheme, carefully keeping the full d dependence originating from the angular parts of the loop integrals. For dimensions less than d<sub>c</sub> = 2 we find a strong–coupling fixed point, which diverges at d = 2, indicating that there is non–perturbative strong– coupling behavior for all d ≥ 2. At d = 1 our method yields the identical fixed point as in the one–loop approximation, and the two–loop contributions to the scaling functions are non–singular. For d > 2 dimensions, there is no finite strong–coupling fixed point. In the framework of a 2 + ϵ expansion, we find the dynamic exponent corresponding to the unstable fixed point, which describes the non–equilibrium roughening transition, to be z = 2 + O (ϵ<sup>3</sup>), in agreement with a recent scaling argument by Doty and Kosterlitz. Similarly, our result for the correlation length exponent at the transition is 1/ν = ϵ + O (ϵ<sup>3</sup>). For the smooth phase, some aspects of the crossover from Gaussian to critical behavior are discussed. | en |
| dc.description.version | Published version | en |
| dc.format.extent | 1024 - 1045 page(s) | en |
| dc.identifier.doi | https://doi.org/10.1103/PhysRevE.50.1024 | en |
| dc.identifier.issn | 1063-651X | en |
| dc.identifier.issue | 2 | en |
| dc.identifier.uri | http://hdl.handle.net/10919/73073 | en |
| dc.identifier.volume | 50 | en |
| dc.relation.uri | http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:A1994PD42500053&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=930d57c9ac61a043676db62af60056c1 | en |
| dc.rights | In Copyright | en |
| dc.rights.uri | http://rightsstatements.org/vocab/InC/1.0/ | en |
| dc.title | Two-Loop Renormalization-Group Analysis of the Burgers-Kardar-Parisi-Zhang Equation | en |
| dc.title.serial | Physical Review E | en |
| dc.type | Article - Refereed | en |
| pubs.organisational-group | /Virginia Tech | en |
| pubs.organisational-group | /Virginia Tech/All T&R Faculty | en |
| pubs.organisational-group | /Virginia Tech/Science | en |
| pubs.organisational-group | /Virginia Tech/Science/COS T&R Faculty | en |
| pubs.organisational-group | /Virginia Tech/Science/Physics | en |