## Abstract

The controversy whether or not the Kardar-Parisi-Zhang (KPZ) equation has an upper critical dimension (UCD) is going on for quite a long time. Some approximate integral equations for the two-point function served as an indication for the existence of a UCD, by obtaining a dimension, above which the equation does not have a strong coupling solution. A surprising aspect of these studies, however, is that various authors who considered the same equation produced large variations in the UCD. This caused some doubts concerning the existence of a UCD. Here we revisit these calculations, describe the reason for such large variations in the results of identical calculations, show by a large-d asymptotic expansion that indeed there exists a UCD and then obtain it numerically by properly defining the integrals involved. Since many difficult problems in condensed matter physics of non-linear nature are handled with mode-coupling and self-consistent theories, this work might also contribute to other researchers working on a large class of different problems that might run into the same inconsistencies.

Original language | American English |
---|---|

Pages (from-to) | 69-78 |

Number of pages | 10 |

Journal | Physica A: Statistical Mechanics and its Applications |

Volume | 309 |

Issue number | 1-2 |

DOIs | |

State | Published - 1 Jun 2002 |

Externally published | Yes |

## Keywords

- KPZ equation
- Upper critical dimension