1. Critical properties of two-particle correlated model.
허희범, 김 엽
경희대학교

2. Motivation 1D Roughening Transition
i) Monomer Deposition - Evaporation Model
(U. Alon, M.R. Evans, H. Hinrichsen and D. Mukamel, Phys. Rev. E. 57 ,4997 (1998))
Normal deposition ( p)
Allow evaporation only at the edges of Terraces (1-p ) p
1-p or
Smooth pC
Rough
( W ~ L )
Active state
Absorbing state
 = the density of vacancies on bottom layer
Active state
Absorbing state
 (pC,L,t) = =
( )
( Directed Percolation (DP) Class ;
0.25, )
0.16

3. ´ ´ p 1-p ii) Dimer Deposition - Evaporation Model Rough Smooth pC2
ii) Dimer Deposition - Evaporation Model
(Haye Hinrichsen and Geza Odor, Phys. Rev. Lett. 82,1205 (1999))
(J.D. Noh, H. Park, M den Nijs, Phys. Rev. Lett. 84, 3891 (2000))
(Modulo 2 conservation)
Rough
Smooth pC
Absorbing state
Active state
( W ~ L )
(Directed Ising (DI) type Transition , )
0.50
0.28
iii) Two-particle correlated growth Model
(Yup Kim,T.S. Kim, and Hyunggyu Park, Phys. Rev. E 66, (2002)) p
1-p
Rough
Smooth pC
Absorbing state
Active state
( W ~ L )

4. What is the Critical Phenomena at critical Point ?3
p  pC
What is the Critical Phenomena at critical Point ?
Monomer Deposition - Evaporation Model DP
Dimer Deposition - Evaporation Model(Modulo 2 conservation) DI
Two-particle correlated growth Model (Modulo 2 conservation) ?

5. p i) Annihilation ii) Branching4
 Model (Two-particle correlated monolayer Model)
Modulo 2 conservation
i) Annihilation p
ii) Branching

6. s(t) : number of survival samples at t5
Simulation results
Static Simulation
 (pC, L, t) = =
s(t) : number of survival samples at t

7.  t ~ 1 / n , n: number of active particles6
p  pC=
 t ~ 1 / n , n: number of active particles

8. 7
Scaling Collapse
pC= , z = 1.74, = 0.292 ) / ( z L t f -

9. t ~ 1 / n2 , n: number of active particles8
Scaling Collapse
t ~ 1 / n2 , n: number of active particles
pC= , = 0.29

10. s(t) : number of survival samples at t9
Dynamic Simulation
s(t) : number of survival samples at t

11. Conclusion Critical Phenomena at critical Point10
Conclusion
Critical Phenomena at critical Point
Monomer Deposition - Evaporation Model DP
Dimer Deposition - Evaporation Model(Modulo 2 conservation) DI
Two-particle correlated growth Model (Modulo 2 conservation)
DP ? or ?

12. 11

13. 12