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

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

´ ´ p 1-p ii) Dimer Deposition - Evaporation Model Rough Smooth pC 2 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 66,046123 (2002)) p 1-p Rough Smooth pC Absorbing state Active state ( W ~ L )

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) ?

p i) Annihilation ii) Branching 4  Model (Two-particle correlated monolayer Model) Modulo 2 conservation i) Annihilation p ii) Branching

s(t) : number of survival samples at t 5 Simulation results Static Simulation  (pC, L, t) = = s(t) : number of survival samples at t

 t ~ 1 / n , n: number of active particles 6 p  pC=0.13807  t ~ 1 / n , n: number of active particles

7 Scaling Collapse pC= 0.13807 , z = 1.74, = 0.292 ) / ( z L t f -

t ~ 1 / n2 , n: number of active particles 8 Scaling Collapse t ~ 1 / n2 , n: number of active particles pC= 0.13807 , = 0.29

s(t) : number of survival samples at t 9 Dynamic Simulation s(t) : number of survival samples at t

Conclusion Critical Phenomena at critical Point 10 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 ?

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