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Universality and criticality of two-particle correlated evolution model

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

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Universality and criticality of two-particle correlated evolution model

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

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

  3. p=1/2 ( = 1/3) r = 1 r facet facet Rough r = 0 pC Smooth 2 Background of this study Directed Percolation (DP) Class with  Dimer deposition/evaporation Model (Modulo 2 conservation) ( H. Hinrichsen and G. Odór, 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 r = 0, p = pC r p r : Digging probability of the particle inside the terraces Satellite Meeting STATPHY 22 in Seoul, Korea Nonequilibrium Statistical Physics of Complex Systems

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

  5. 4 Background of this study 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 !! Satellite Meeting STATPHY 22 in Seoul, Korea Nonequilibrium Statistical Physics of Complex Systems

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

  7. 5 Simulation results Simulation results s(t) : number of survival samples at t L = 105, T=107 Satellite Meeting STATPHY 22 in Seoul, Korea Nonequilibrium Statistical Physics of Complex Systems

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

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

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

  11. Satellite Meeting STATPHY 22 in Seoul, Korea Nonequilibrium Statistical Physics of Complex Systems 9 Simulation results L = 105, T=107

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

  13. Satellite Meeting STATPHY 22 in Seoul, Korea Nonequilibrium Statistical Physics of Complex Systems 11 Simulation results L = 105, T=107

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

  15. Satellite Meeting STATPHY 22 in Seoul, Korea Nonequilibrium Statistical Physics of Complex Systems 13 Simulation results (Preliminary results) L = 29 At pc=0.1044 ,

  16. Satellite Meeting STATPHY 22 in Seoul, Korea Nonequilibrium Statistical Physics of Complex Systems 14 Conclusion Conclusion 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?

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