## Abstract

In this paper, I analyze a generalization of the molecular-beam-epitaxy equation (with spatially correlated noise) that takes into account long-range interactions of a volume conserving surface. This equation is, therefore, called the non-local molecular-beam-epitaxy (NMBE) equation, sometimes also known as the non-local conserved Kardar-Parisi-Zhang equation. I find an exact result for a subfamily of the NMBE models in one dimension. I then compare this exact result to a previous result obtained by Jung et al. (Phys. Rev. E 62 (2000) 2949) who applied a dynamic renormalization group (DRG) analysis to this problem. I show explicitly that this approach does not yield the exact result I obtain. This example suggests that one should be careful when applying DRG to nonlinear continuum equations.

Original language | American English |
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Pages (from-to) | 25-28 |

Number of pages | 4 |

Journal | Physica A: Statistical Mechanics and its Applications |

Volume | 308 |

Issue number | 1-4 |

DOIs | |

State | Published - 15 May 2002 |

Externally published | Yes |

## Keywords

- Exact result
- KPZ equation
- Molecular beam epitaxy
- Nonlocal models