Surface growth with long-range correlated noise

Amar, Jacques G.; Lam, Pui-Man; Family, Fereydoon

doi:10.1103/physreva.43.4548

Cited by 56 publications

(32 citation statements)

References 13 publications

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“…The first systematic numerical work done on spatially correlated noise is due to Amar, Lam and Family [20]. Their results are in agreement with the dynamical [21] and functional RG [22,23] predictions.…”

Section: Introductionsupporting

confidence: 73%

Universal properties of shortest paths in isotropically correlated random potentials

Schorr

Rieger

2003

The European Physical Journal B - Condensed Matter

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Abstract. We consider the optimal paths in a d-dimensional lattice, where the bonds have isotropically correlated random weights. These paths can be interpreted as the ground state configuration of a simplified polymer model in a random potential. We study how the universal scaling exponents, the roughness and the energy fluctuation exponent, depend on the strength of the disorder correlations. Our numerical results using Dijkstra's algorithm to determine the optimal path in directed as well as undirected lattices indicate that the correlations become relevant if they decay with distance slower than 1/r in d = 2 and 3. We show that the exponent relation 2 ν − ω = 1 holds at least in d = 2 even in case of correlations. Both in two and three dimensions, overhangs turn out to be irrelevant even in the presence of strong disorder correlations.

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Section: Introductionsupporting

confidence: 73%

Universal properties of shortest paths in isotropically correlated random potentials

Schorr

Rieger

2003

The European Physical Journal B - Condensed Matter

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“…For d = 1, early simulations [19] using restricted solid-onsolid (RSOS) and ballistic deposition models, seemed to strongly support the predictions of the dynamic RG calculation with ρ c = 1 4 . These results, however, could not be confirmed by later simulations using complementary models [20].…”

Section: Introductionmentioning

confidence: 55%

Exact results for the Kardar-Parisi-Zhang equation with spatially correlated noise

1999

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We investigate the Kardar-Parisi-Zhang (KPZ) equation in d spatial dimensions with Gaussian spatially long-range correlated noise -characterized by its second moment R(x − x ) ∝ |x − x | 2ρ−d -by means of dynamic field theory and the renormalization group. Using a stochastic Cole-Hopf transformation we derive exact exponents and scaling functions for the roughening transition and the smooth phase above the lower critical dimension dc = 2(1 + ρ). Below the lower critical dimension, there is a line ρ * (d) marking the stability boundary between the short-range and long-range noise fixed points. For ρ ≥ ρ * (d), the general structure of the renormalization-group equations fixes the values of the dynamic and roughness exponents exactly, whereas above ρ * (d), one has to rely on some perturbational techniques. We discuss the location of this stability boundary ρ * (d) in light of the exact results derived in this paper, and from results known in the literature. In particular, we conjecture that there might be two qualitatively different strong-coupling phases above and below the lower critical dimension, respectively.

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“…These include discrete one-dimensional models [ballistic deposition (BD) [5][6][7], solid-on-solid (SOS) [7,8], and direct (discrete) integration of the KPZ equation [5]]. Many researchers studied the KPZ equation with such noise [9][10][11][12][13][14][15][16] and obtained different predictions.…”

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confidence: 99%

Kardar-Parisi-Zhang equation with temporally correlated noise: A self-consistent approach

Katzav

Schwartz

2004

Phys. Rev. E

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In this paper we discuss the well known Kardar-Parisi-Zhang (KPZ) equation driven by temporally correlated noise. We use a self-consistent approach to derive the scaling exponents of this system. We also draw general conclusions about the behavior of the dynamic structure factor Phiq(t) as a function of time. The approach we use here generalizes the well known self-consistent expansion (SCE) that was used successfully in the case of the KPZ equation driven by white noise, but unlike SCE, it is not based on a Fokker-Planck form of the KPZ equation, but rather on its Langevin form. A comparison to two other analytical methods, as well as to the only numerical study of this problem is made, and a need for an updated extensive numerical study is identified. We also show that a generalization of this method to any spatiotemporal correlations in the noise is possible, and two examples of this kind are considered.

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Surface growth with long-range correlated noise

Cited by 56 publications

References 13 publications

Universal properties of shortest paths in isotropically correlated random potentials

Universal properties of shortest paths in isotropically correlated random potentials

Exact results for the Kardar-Parisi-Zhang equation with spatially correlated noise

Kardar-Parisi-Zhang equation with temporally correlated noise: A self-consistent approach

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