2-Dimensional Multi-Site-Correlated Surface Growths with Restricted Solid-on-Solid Condition. (이차원 기판 위에서 다입자 상관 성장 모형의 축척 특성) 김 택수, 김 엽(경희대)

Motivation of Study (1) Is Anomalous Roughness Really happening ? (Deok-Sun Lee and Marcel den Nijs, Phys. Rev. E 65, 026104 (2002)) (2) The better growth patterns corresponding to mulitply-correalated 2d Membrane

2  2d Model  The growth rule for the -site correlated growth <1> Select columns { } (  2) randomly. <2-a> If then for =1,2..., with a probability p. for =1,2..., with q =1-p. With restricted solid-on-solid(RSOS)condition, <2-b> then new selection of columns is taken.  The dissociative -mer growth ▶ A special case of the -site correlated growth. Select conneted columns  Dimer model : with/without monomer diffusion on terraces (Schwoebel barrier)

3 (1) Dimer (2) 2-site (3) Trimer (4) 3-site  An arbitrary combination of (2, 3) sites of the same height  Nonlocal topological constraint : All height levels must be occupied by an (2,3)-multiple number of sites. Mod (2,3) conservation of site number at each height level. (1) Dimer (2) 2-site p q q p (3) Trimer (4) 3-site q p p q

 Physical Backgrounds for This Study 4  Physical Backgrounds for This Study Steady state or Saturation regime, Simple RSOS with ( equilibrium state ) Normal RSOS Model (EW Universality class)  =-1, nh=even number, Anomalous Roughening ? Normal ?

5  1d L   , Ergodicity problem eff eff  1 k-mer (faceted) 1. p = q = 1/2 (equilibrium state)  1/3 ( k-site, 3,4-mer)  1/3 (Dimer growth model) Ergodicity problem 2. p ≠ q (growing or eroding phase)  1 k-mer (faceted) (J. D. Noh, H. Park, Doochul Kim and M. den Nijs, PRE. (2001))  1 k-site (groove formation ) L   , eff eff ? eff eff

( Monomer,k-site,Trimer, Dimer & Monomer Diffusion) 6  2d (Dimer model) (Deok-Sun Lee and Marcel den Nijs, Phys. Rev. E 65,026104(2002)) ? ( Monomer,k-site,Trimer, Dimer & Monomer Diffusion) Scaling Theory for Normal Roughening Case

Slope a 7 2d Simulation Results Dimer & 2-site & Monomer Model Monomer 0.162 Dimer 0.175 Monomer Slope a Model 2-site 0.176

Dimer & Dimer-Monomer Diffusion &Monomer 8 Dimer & Dimer-Monomer Diffusion &Monomer 0.162 Dimer 0.175 Monomer Slope a Model 0.177 Dimer & Monomer- Diffusion

9 3-site & Monomer 0.173 3-site 0.175 Monomer Slope a Model

10 Trimer & Monomer 0.174 Triemr 0.175 Monomer Slope a Model

Monomer & Extremal & Dimer & 2-site 11 Monomer & Extremal & Dimer & 2-site 0.175 0.162 Dimer Monomer Slope a Model Extremal 0.174 2-site

Scaling Collapse ( 2-site model z = 2.4 ) 12 Scaling Collapse ( 2-site model z = 2.4 )

??? 13 Conclusion  k-site, Trimer model Slope a  0.175 Dimer model Slope a  0.162  Dimer & Monomer-Diffusion Slope a  0.175  In d =2, Dynamic exponent z ( 2-site model )  2.4 (?) ???  =-1  = 0  = 1 Multiply-Correlated Membrane Extremal growth Normal Random Membrane