Equilibrium-restricted solid-on-solid growth model on fractal substrates

2013

Self Cite

Absorbing phase transitions in the conserved threshold transfer process (CTTP) on diluted lattices, i.e., on infinite percolation networks, were studied in two dimensions by Monte Carlo simulations. Lattice dilution was found to be irrelevant to the critical behavior for the concentration of diluted sites x far less than the critical concentration x c (=1 − p c , with p c being the percolation threshold), whereas for x close to x c the critical exponents slightly deviated from those of the pure CTTP and new critical exponents were established at x c . The results for x < x c were consistent with the recent results for the conserved lattice gas (CLG) model, whereas the results for x = x c were different from those of the CLG model, for which nonuniversal power-law behavior was observed [Lee, Phys. Rev. E 84, 041123 (2011)]. On the other hand, the critical exponents of the CTTP on a percolation backbone were similar to those on an infinite network and similar to those of the CLG model on a backbone network. The diluted CTTP in three and four dimensions was also investigated, and the critical exponents were similar to those in two dimensions; i.e., the critical exponents were independent of or weakly dependent on the dimensionality. A comment on the recent claim of the absence of a Manna class was also presented.

Section: Discussionsupporting

confidence: 74%

Absorbing phase transitions in diluted conserved threshold transfer process

Lee

2013

Self Cite

“…(6) by power counting method. If a system is rescaled by a factor "b" (i.e., x → bx), then h → b α h, t → b z t, and the conserved noise η c is rescaled as η c → b −(d f +z+z rw )/2 η c [19,20]. Therefore, Eq.…”

Section: Conserved Noise Restricted Solid-on-solid On Fractal Submentioning

confidence: 99%

Conserved noise restricted-solid-on-solid model on fractal substrates

2011

Self Cite

A conserved noise restricted solid-on-solid model on both a Sierpinski gasket substrate and a checkerboard fractal substrate is studied. The interface width W grows as t(β) at early time t and becomes saturated at L(α) for t >> L(z), where L is the system size. We obtain β ≈ 0.0788, α ≈ 0.377 for a Sierpinski gasket, and β ≈ 0.100, α ≈ 0.516 for a checkerboard fractal. The dynamic exponent z ≈ 4.79 for a Sierpinski gasket and z ≈ 5.16 for a checkerboard fractal are obtained by the relation z = α/β. They satisfy the scaling relations 4 α + 2 d(f) = z and z = 2 z(rw), where z(rw) is the random-walk exponent of the fractal substrate. A fractional Langevin equation is introduced to describe the model.

“…This scaling relation is believed to be related to the tilting symmetry of the KPZ equation [4]. Breakdown of the scaling relation has been reported before for the surfaces with random impurities [8,10,21,22]. Actually, the quenched randomness seems to break the scaling relation.…”

Section: Random Tiling With Tile-type Dependent Sticking Probabilimentioning

confidence: 62%

“…Actually, quenched defects on periodic substrates can change surface morphology dramatically. If the quenched defects break the translational symmetry of the periodic structures, RSOS growth on such a substrate may not show the KPZ universality characteristics [8][9][10]. Here, we investigate whether the translation symmetry of periodicity in the substrate is necessary for RSOS growth to be the KPZ class or not.…”

Section: Introductionmentioning

confidence: 99%

Surface scaling properties of decagonal quasicrystals under nonequilibrium vertical growth

Jeong

2012

Self Cite

Restricted solid-on-solid (RSOS) growth models are studied on two different decagonal quasicrystal lattices, namely the Penrose tiling lattice and the random tiling lattice. There exist two types of growth blocks-fat and skinny tiles-which may have different sticking probabilities. We found that the RSOS growths on both lattices belong to the Kardar-Parisi-Zhang universality class when they have the same sticking probabilities in spite of the lack of periodicity in the substrates. However, when they have tile-type dependent sticking probabilities, the RSOS models on two lattices may produce different scaling behaviors. Growth on Penrose tiling shows that the roughness exponent is around 0.4 while that on random tiling is around 0.49. Our observation may provide an effective way to investigate the bulk structures of decagonal quasicrystals.