TY - JOUR

T1 - Exact result vs. dynamic renormalization group analysis for the nonlocal molecular-beam-epitaxy equation

AU - Katzav, Eytan

PY - 2002/5/15

Y1 - 2002/5/15

N2 - 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.

AB - 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.

KW - Exact result

KW - KPZ equation

KW - Molecular beam epitaxy

KW - Nonlocal models

UR - http://www.scopus.com/inward/record.url?scp=0037092921&partnerID=8YFLogxK

U2 - 10.1016/S0378-4371(02)00589-7

DO - 10.1016/S0378-4371(02)00589-7

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AN - SCOPUS:0037092921

SN - 0378-4371

VL - 308

SP - 25

EP - 28

JO - Physica A: Statistical Mechanics and its Applications

JF - Physica A: Statistical Mechanics and its Applications

IS - 1-4

ER -