1. Universality and criticality of two-particle correlated evolution model S. Y. Yoon and Yup Kim Department of Physics, Kyung-Hee University Satellite Meeting STATPHY 22 in Seoul, Korea Nonequilibrium Statistical Physics of Complex Systems

2. Background of this study  1D Roughening Transition (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  = the density of vacancies on bottom layer Active state Absorbing state RoughSmooth pCpC Absorbing state Active state ( W ~ L  )  Monomer deposition/evaporation Model Satellite Meeting STATPHY 22 in Seoul, Korea Nonequilibrium Statistical Physics of Complex Systems or p 1-p Background of this study 1

3.  Dimer deposition/evaporation Model (Modulo 2 conservation) ( H. Hinrichsen and G. Od ó r, Phys. Rev. Lett. 82,1205 (1999), J. D. Noh, H. Park, M den Nijs, Phys. Rev. Lett. 84, 3891 (2000) )  Directed Ising (DI) type Transition with Satellite Meeting STATPHY 22 in Seoul, Korea Nonequilibrium Statistical Physics of Complex Systems Background of this study 2  Directed Percolation (DP) Class with r = 0, p = p C r p r = 1 r = 0 pCpC p=1/2 (  = 1/3) Smooth facet Rough facet r r : Digging probability of the particle inside the terraces

4.  Two-particle correlated growth Model 1. r = 1 (Yup Kim,T.S. Kim, and Hyunggyu Park, Phys. Rev. E 66,046123 (2002)) groove  = 1 p = 1/2 groove  = 1 r p r : Digging probability of the particle inside the terraces r = 1 r = 0 pcpc  = 1/3 Smooth ?(rougheing) p 1-p p = q (q=1-p),  L → ∞ ) p  q,  L → ∞ ) Dynamical Scaling Law for Kinetic Surface Roughening Satellite Meeting STATPHY 22 in Seoul, Korea Nonequilibrium Statistical Physics of Complex Systems Background of this study 3

5. Satellite Meeting STATPHY 22 in Seoul, Korea Nonequilibrium Statistical Physics of Complex Systems Background of this study 4 2. r = 0 1) Is there Roughening Transition for r = 0 ? 2) 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)  ? To answer the questions, we should first study the two particles correlated monolayer model !!

6. q Model ( Two-particle correlated monolayer Model ) i) Annihilation ii) Branching Most general model with modulo-2 conservation of particles. Satellite Meeting STATPHY 22 in Seoul, Korea Nonequilibrium Statistical Physics of Complex Systems Model 5

7. Simulation results s(t) : number of survival samples at t Satellite Meeting STATPHY 22 in Seoul, Korea Nonequilibrium Statistical Physics of Complex Systems Simulation results 5 L = 10 5, T=10 7

9. Satellite Meeting STATPHY 22 in Seoul, Korea Nonequilibrium Statistical Physics of Complex Systems Simulation results 6

10. Satellite Meeting STATPHY 22 in Seoul, Korea Nonequilibrium Statistical Physics of Complex Systems  Dimer type (DI class) q i) Annihilation ii) Branching Simulation results 7

11. Satellite Meeting STATPHY 22 in Seoul, Korea Nonequilibrium Statistical Physics of Complex Systems  Case 1 i) Annihilation ii) Branching Simulation results q 8

12. Satellite Meeting STATPHY 22 in Seoul, Korea Nonequilibrium Statistical Physics of Complex Systems Simulation results 9 L = 10 5, T=10 7

13. Satellite Meeting STATPHY 22 in Seoul, Korea Nonequilibrium Statistical Physics of Complex Systems Simulation results  Case 2 i) Annihilation ii) Branching q 10

14. Satellite Meeting STATPHY 22 in Seoul, Korea Nonequilibrium Statistical Physics of Complex Systems Simulation results 11 L = 10 5, T=10 7

15. Satellite Meeting STATPHY 22 in Seoul, Korea Nonequilibrium Statistical Physics of Complex Systems  Two-particle correlated type growth model Simulation results (Preliminary results) 12 L = 32, 64, 128, 256, 512

16. Satellite Meeting STATPHY 22 in Seoul, Korea Nonequilibrium Statistical Physics of Complex Systems Simulation results (Preliminary results) 13 L = 2 9 At p c =0.1044,

17. Conclusion Satellite Meeting STATPHY 22 in Seoul, Korea Nonequilibrium Statistical Physics of Complex Systems Conclusion 1414 1. 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? Class  / ||  /  z DI0.2850.51.75 DP0.1590.2521.58 Two-particle Model0.159  0.25 PCPD~0.20