1. 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)

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

3. 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)

4. 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

5.  Physical Backgrounds for This Study4
 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 ?

6. 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

7. ( 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

8. 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

9. Dimer & Dimer-Monomer Diffusion &Monomer8
Dimer & Dimer-Monomer Diffusion &Monomer
0.162
Dimer
0.175
Monomer
Slope a
Model
0.177
Dimer & Monomer-
Diffusion

10. 9
3-site & Monomer
0.173
3-site
0.175
Monomer
Slope a
Model

11. 10
Trimer & Monomer
0.174
Triemr
0.175
Monomer
Slope a
Model

12. Monomer & Extremal & Dimer & 2-site11
Monomer & Extremal & Dimer & 2-site
0.175
0.162
Dimer
Monomer
Slope a
Model
Extremal
0.174
2-site

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

14. ??? 13 Conclusion  k-site, Trimer model Slope a  0.175
Dimer model Slope a  0.162
 Dimer & Monomer-Diffusion Slope a 
 In d =2, Dynamic exponent z ( 2-site model )  2.4 (?)
???
 =-1
 = 0
 = 1
Multiply-Correlated
Membrane
Extremal
growth
Normal Random
Membrane