On the renormalization of the KardarParisiZhang equation
Abstract
The KardarParisiZhang (KPZ) equation of nonlinear stochastic growth in d dimensions is studied using the mapping onto a system of directed polymers in a quenched random medium. The polymer problem is renormalized exactly in a minimally subtracted perturbation expansion about d = 2. For the KPZ roughening transition in dimensions d > 2, this renormalization group yields the dynamic exponent z^{★} = 2 and the roughness exponent χ^{★} = 0, which are exact to all orders in ɛ ≡ (2  d)/2. The expansion becomes singular in d = 4. If this singularity persists in the strongcoupling phase, it indicates that d = 4 is the upper critical dimension of the KPZ equation. Further implications of this perturbation theory for the strongcoupling phase are discussed. In particular, it is shown that the correlation functions and the coupling constant defined in minimal subtraction develop an essential singularity at the strongcoupling fixed point.
 Publication:

Nuclear Physics B
 Pub Date:
 February 1995
 DOI:
 10.1016/05503213(95)00268W
 arXiv:
 arXiv:condmat/9501094
 Bibcode:
 1995NuPhB.448..559L
 Keywords:

 Condensed Matter
 EPrint:
 21 pp. (latex, now texable everywhere, no other changes), with 2 fig.