SCALING APPROACH TO THE ANISOTROPIC NONLOCAL KARDAR–PARISI–ZHANG EQUATION WITH SPATIALLY CORRELATED NOISE

2002 ◽  
Vol 16 (04) ◽  
pp. 563-569 ◽  
Author(s):  
GANG TANG ◽  
BENKUN MA
Keyword(s):  
Renormalization Group ◽  
Strong Coupling ◽  
Weak Coupling ◽  
Group Analysis ◽  
Correlated Noise ◽  
Scaling Exponents ◽  
Coupling Region ◽  
Renormalization Group Analysis ◽  
Spatially Correlated ◽  
Spatially Correlated Noise

The scaling approach proposed by Hentschel and Family [Phys. Rev. Lett.66, 1982 (1991)] is generalized to the studies of the scaling of the anisotropic nonlocal Kardar–Parisi–Zhang equation with spatially correlated noise. The scaling exponents in both the weak- and strong-coupling regions are obtained, respectively. The scaling exponents obtained in the weak-coupling region can well match the results of the dynamic renormalization-group analysis.

SURFACE GROWTH WITH TEMPORALLY CORRELATED NOISE

Fractals ◽  
1993 ◽  
Vol 01 (01) ◽  
pp. 1-9 ◽  
Author(s):  
CHI-HANG LAM ◽  
LEONARD M. SANDER ◽  
DIETRICH E. WOLF
Keyword(s):  
Chaotic Map ◽  
Correlated Noise ◽  
Kpz Equation ◽  
Scaling Exponents ◽  
Spatially Correlated ◽  
Power Law Noise ◽  
Temporally Correlated ◽  
Spatially Correlated Noise ◽  
Anomalous Growth ◽  
Good Agreement

We simulate ballistic deposition with long range temporally correlated noise of bounded amplitude in 1 + 1 dimension. Good agreement with the dynamical renormalization group calculation of Medina et al. is obtained for the scaling exponents when the noise is generated by a version of Mandelbrot's fast fractional Gaussian noise (ffGn) generator. However, using either the original ffGn or a chaotic map generator, other exponents are obtained. We suggest that this difference is due to an extraordinarily slow crossover caused by the existence of an anomalous growth mode incompatible with the KPZ equation. This may have implications on similar model dependent results for recent simulations on growth with power-law noise and spatially correlated noise.

RENORMALIZATION GROUP METHODS IN CONSTRUCTIVE FIELD THEORIES

2000 ◽  
Vol 14 (12n13) ◽  
pp. 1363-1398
Author(s):  
HIROSHI WATANABE
Keyword(s):  
Renormalization Group ◽  
Group Analysis ◽  
Group Method ◽  
Coupling Region ◽  
Renormalization Group Analysis ◽  
New Approach ◽  
Group Methods ◽  
Technical Details ◽  
Hierarchical Approximation

Mathematical construction of quantum field theory is reviewed with emphasis on the conceptual structure of the construction and on the role of rigorous renormalization group analysis without technical details. After explaining a rigorous formulation of a renormalization group method in a weak coupling region, a new approach in a strong coupling region is proposed in the context of the hierarchical approximation. An idea of proving triviality in d≥4 dimensions utilizing this new proposal concludes this review.

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