The non-equilibrium phase transition of the pair-contact process with diffusion

Journal of Physics A: Mathematical and General

Volumn 37, Issue 28, 2004, Pages

  Henkel, Malte ^a   Hinrichsen, Haye ^b  

^a INSTITUT JEAN LAMOUR   (France)

^b UNIVERSITY OF WÜRZBURG   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 3242672561     PISSN: 03054470     EISSN: None     Source Type: Journal    
DOI: 10.1088/0305-4470/37/28/R01     Document Type: Article

References (104)

1. Marro J and Dickman R 1999 Non-Equilibrium Phase Transitions in Lattice Models (Cambridge: Cambridge University Press)
2. Hinrichsen H 2000 Non-equilibrium critical phenomena and phase transitions into absorbing states Adv. Phys. 49 815
3. Mendes J F F, Dickman R, Henkel M and Marques M C 1994 Generalized scaling for models with multiple absorbing states J. Phys. A: Math. Gen. 27 3019
4. Harris T E 1974 Contact interactions on a lattice Ann. Prob. 2 969
5. Kinzel W 1983 Percolation structures and processes Ann. Isr. Phys. Soc. vol 5, ed G Deutscher, R Zallen and J Adler, (Bristol: Adam Hilger)
6. Liggett T M 1985 Interacting Particle Systems (Heidelberg: Springer)
7. Ódor G 2004 Universality classes in non-equilibrium lattice systems Preprint cond-mat/0205644 (Rev. Mod. Phys. 76 at press)
8. Zhong D and ben Avraham D 1995 Universality class of two-offspring branching annihilating random walks Phys. Lett. A 209 333
9. Cardy J and Täuber U C 1996 Theory of branching and annihilating random walks Phys. Rev. Lett. 77 4780
10. Dornic I, Chaté H, Chave J and Hinrichsen H 2001 Critical coarsening without surface tension: the voter universality class Phys. Rev. Lett. 87 5701
11. Droz M, Ferreira A L and Lipowski A 2003 Splitting the voter criticality Phys. Rev. E 67 056108
12. Cardy J L and Grassberger P 1985 Epidemic models and percolation J. Phys. A: Math. Gen. 18 L267
13. Janssen H K 1985 Renormalized field theory of dynamical percolation Z. Phys. B 58 311
14. Rossi M, Pastor-Satorras R and Vespignani A 2000 Universality class of absorbing phase transitions with a conserved field Phys. Rev. Lett. 85 1803
15. Lübeck S 2002 Scaling behaviour of the order parameter and its conjugated field in an absorbing phase transition around the upper critical dimension Phys. Rev. E 65 046150
16. Lübeck S and Heger PC 2003 Universal scaling behaviour at the upper critical dimension of non-equilibrium continuous phase transitions Phys. Rev. Lett. 90 230601
17. Jensen I 1993 Critical behaviour of the pair-contact process Phys. Rev. Lett. 70 1465
18. Jensen I and Dickman R 1993 Non-equilibrium phase transitions in systems with infinitely many absorbing states Phys. Rev. E 48 1710
19. Carlon E, Henkel M and Schollwöck U 2001 Critical properties of the reaction-diffusion model 2A → 3A, 2A → Ø Phys. Rev. E 63 036101
20. Dickman R and Kamphorst Leal da Silva J 1998 Moment ratios for absorbing-state phase transitions Phys. Rev. E 58 4266
21. Kamphorst Leal da Silva J and Dickman R 1999 Pair-contact process in two dimensions Phys. Rev. E 60 5126
22. Lübeck S and Willmann R D 2002 Universal scaling behaviour of directed percolation and the pair-contact process in an external field J. Phys. A: Math. Gen. 35 10205
23. Grassberger P and de la Torre A 1979 Reggeon field theory (Schlögl's first model) on a lattice: Monte Carlo calculations of critical behaviour Ann. Phys., NY 122 373-96
24. Janssen H K 1981 On the non-equilibrium phase transition in reaction-diffusion systems with an absorbing stationary state Z. Phys. B 42 151
25. López C and Muñoz M A 1997 Numerical analysis of a Langevin equation for systems with infinite absorbing states Phys. Rev. E 56 4864
26. Jimenez-Dalmaroni A and Hinrichsen H 2003 Epidemic processes with immunization Phys. Rev. E 68 036103
27. Muñoz M A, Grinstein G, Dickman R and Livi R 1996 Critical behaviour of systems with many absorbing states Phys. Rev. Lett. 76 451
28. van Wijland F 2002 Universality class of non-equilibrium phase transitions with infinitely many absorbing states Phys. Rev. Lett. 89 190602
29. Dickman R 1989 Universality and diffusion in non-equilibrium critical phenomena Phys. Rev. B 40 7005
30. Grassberger P 1982 On phase transitions in Schlögl's second model Z. Phys. B 47 365
31. Howard M J and Täuber U C 1997 'Real' versus 'imaginary' noise in diffusion-limited reactions J. Phys. A: Math. Gen. 30 7721
32. Henkel M and Mendes J F F 1996 unpublished
33. White S R 1992 Density-matrix formulation for quantum renormalization groups Phys. Rev. Lett. 69 2863
34. White S R 1993 Density-matrix algorithms for quantum renormalization groups Phys. Rev. B 48 10345
35. Schollwöck U 2004 Density-matrix renormalization group Rev. Mod. Phys. at press
36. Kaulke M and Peschel I 1998 A DMRG study of the q-symmetric Heisenberg chain Eur. Phys. J. B 5 727
37. Carlon E, Henkel M and Schollwöck U 1999 Density-matrix renormalization group and reaction-diffusion processes Eur. Phys. J. B 12 99
38. Hinrichsen H 2001 Pair-contact process with diffusion: a new type of non-equilibrium critical behaviour? Phys. Rev. E 63 036102
39. Ódor G 2000 Critical behaviour of the one-dimensional annihilation-fission process 2A → Ø, 2A → 3A Phys. Rev. E 62 R3027
40. Hinrichsen H 2001 Cyclically coupled spreading and pair-annihilation Physica A 291 275
41. Ódor G 2001 Phase transition of the one-dimensional coagulation-production process Phys. Rev. E 63 067104
42. Park K, Hinrichsen H and Kim I-M 2001 Binary spreading process with parity conservation Phys. Rev. E 63 R065103
43. Henkel M and Hinrichsen H 2001 Exact solution of a reaction-diffusion process with three-site interactions J. Phys. A: Math. Gen. 34 1561
44. Henkel M and Schollwöck U 2001 Universal finite-size scaling amplitudes in anisotropic scaling J. Phys. A: Math. Gen. 34 3333
45. Ódor G, Marques M C and Santos M A 2002 Phase transition of a two-dimensional binary spreading model Phys. Rev. E 65 056113
46. Ódor G 2002 Multicomponent binary spreading process Phys. Rev. E 66 026121
47. Noh J D and Park H 2004 Novel universality class of absorbing transitions with continuously varying exponents Phys. Rev. E 69 016122
48. Park K and Kim I-M 2002 Well-defined set of exponents for a pair-contact process with diffusion Phys. Rev. E 66 027106
49. Dickman R and de Menezes M A F 2002 Nonuniversality in the pair-contact process with diffusion Phys. Rev. E 66 045101
50. Hinrichsen H 2003 Stochastic cellular automaton for the coagulation-fission process 2A → 3A, 2A → A Physica A 320 249
51. Kockelkoren J and Chaté H 2003 Absorbing phase transition of branching-annihilating random walks Phys. Rev. Lett. 90 125701
52. Ódor G 2003 Critical behaviour of the one-dimensional diffusive pair-contact process Phys. Rev. E 67 016111
53. Paessens M and Schütz G M 2004 Phase transitions and correlations in the bosonic pair-contact process with diffusion: exact results J. Phys. A: Math. Gen. 37 4709
54. Barkema G T and Carlon E 2003 Universality in the pair-contact process with diffusion Phys. Rev. E 68 036113
55. Hinrichsen H 2003 The diffusive pair-contact process and non-equilibrium wetting, unpublished notes Preprint cond-mat/0302381
56. Ódor G 2004 Private communication
57. Toussaint D and Wilczek F 1983 Particle-antiparticle annihilation in diffusive motion J. Chem. Phys. 78 2642
58. Muñoz M, Grinstein G and Tu Y 1997 Survival probability and field theory in systems with absorbing states Phys. Rev. E 56 5101
59. Jensen I 1999 Low-density series expansions for directed percolation: 1. A new efficient algorithm with applications to the square lattice J. Phys. A: Math. Gen. 32 5233
60. ben Avraham D and Köhler J 1992 Mean-field (n, m)-cluster approximation for lattice models Phys. Rev. A 45 8358
61. Gutowitz H A, Victor J D and Knight B W 1987 Local structure theory for cellular automata Physica D 28 18
62. Dickman R 1988 Mean-field theory of the driven diffusive lattice gas Phys. Rev. A 38 2588
63. Houchmandzadeh B 2002 Clustering of diffusing organisms Phys. Rev. E 66 052902
64. Henkel M 2003 On lower bounds of the solutions of some simple reaction-diffusion equations Preprint math-ph/0309027
65. Grassberger P 1999 Private communication
66. Marques M C, Santos M A and Mendes J F F 2001 Static critical behaviour in the inactive phase of the pair-contact process Phys. Rev. E 65 066110
67. Dickman R, Rabêlo W R M and Ódor G 2002 Pair-contact process with a particle source Phys. Rev. E 65 016118
68. Szolnoki A 2002 Dynamical mean-field approximation for a pair-contact process with a particle source Phys. Rev. E 66 057102
69. Schütz G M 2000 Exactly solvable models for many-body systems far from equilibrium Phase Transitions and Critical Phenomena vol 19, ed C Domb and J L Lebowitz (London: Academic)
70. Henkel M 2003 Reaction-diffusion processes and their connection with integrable quantum spin chains Classical and Quantum Nonlinear Integrable Systems: Theory and Applications ed A Kundu (Bristol: Institute of Physics Publishing) p 256
71. Privman V (ed) 1990 Finite-Size Scaling and Numerical Simulation of Statistical Systems (Singapore: World Scientific)
72. Lauritsen K B, Fröjdh P and Howard M 1998 Surface critical behaviour in systems with absorbing states Phys. Rev. Lett. 81 2104
73. Fröjdh P, Howard M and Lauritsen K B 1998 Directed percolation with a wall or edge J. Phys. A: Math. Gen. 31 2311
74. Bulirsch R and Stoer J 1964 Fehlerabschätzungen und Extrapolation mit rationalen Funktionen bei Verfahren vom Richardson-Typus Numer. Math. 6 413
75. Henkel M and Schütz G 1988 Finite-lattice extrapolation algorithms J. Phys. A: Math. Gen. 21 2617
76. Hinrichsen H 2003 Roughening transition driven by a binary spreading process Eur. Phys. J. B 31 365
77. Mendes J F F 1996 Private communication
78. van Wijland F, Oerding K and Hilhorst H J 1998 Wilson renormalization of a reaction-diffusion process Physica A 251 179
79. ben Avraham D, Burschka M and Doering C R 1990 Statics and dynamics of a diffusion-limited reaction: anomalous kinetics, non-equilibrium self-ordering and a dynamic transition J. Stat. Phys. 60 695
80. Privman V and Fisher M E 1984 Universal critical amplitudes in finite-size scaling Phys. Rev. B 30 322
81. Privman V, Hohenberg P C and Aharony A 1993 Universal critical-point amplitude relations Phase Transitions and Critical Phenomena vol 14, ed C Domb and J L Lebowitz (London: Academic)
82. Barber M N and Hamer C J 1982 Extrapolation of sequences using a generalized epsilon algorithm J. Aust. Math. Soc. B 23 229
83. Fröjdh P, Howard M and Lauritsen K B 2001 Directed percolation and systems with absorbing states: impact of boundaries Int. J. Mod. Phys. B 15 1761
84. Essam J W, Guttmann A J, Jensen I and Tanlakishani D 1996 Directed percolation near a wall J. Phys. A: Math. Gen. 29 1619
85. Park K 2003 Private communication
86. Alon U, Evans M R, Hinrichsen H and Mukamel D 1998 Roughening transition in a one-dimensional growth process Phys. Rev. Lett. 76 2746
87. Alon U, Evans M R, Hinrichsen H and Mukamel D 1998 Smooth phases, roughening transitions and novel exponents in one-dimensional growth models Phys. Rev. E 57 4997
88. Hinrichsen H and Ódor G 1999 Roughening transition in a model for dimer adsorption and desorption Phys. Rev. Lett. 82 1205
89. Hinrichsen H and Ódor G 1999 Critical behaviour of roughening transitions in parity-conserving growth processes Phys. Rev. E 60 3842
90. Goldschmidt Y Y, Hinrichsen H, Howard M J and Täuber U C 1999 Novel non-equilibrium critical behaviour induced by unidirectional coupling of stochastic processes Phys. Rev. E 59 6381
91. Deloubrière O, Janssen H K, Täuber U C and Wijland F 2004 Private communication
92. Lee B P 1994 Renormalization group calculation for the reaction kA → Ø J. Phys. A: Math. Gen. 27 2633
93. Janssen H K and Täuber U C 2004 Private communication
94. van Wijland F 2001 Field theory for reaction-diffusion processes with hard-core particles Phys. Rev. E 63 022101
95. Park K, Hinrichsen H and Kim I-M 2002 Phase transition in a triplet process Phys. Rev. E 65 R025101
96. Young R W, Roberts A J and Stuhne G 2001 Reproductive pair correlations and the clustering of organisms Nature 412 328
97. Godrèche C and Luck J-M 2001 Response of non-equilibrium systems at criticality: ferromagnetic models in dimension two and above J. Phys. A: Math. Gen. 33 9141
98. Picone A and Henkel M 2002 Response of non-equilibrium systems with long-range initial correlations J. Phys. A: Math. Gen. 35 5572
99. Paessens M and Henkel M 2003 The kinetic spherical model in a magnetic field J. Phys. A: Math. Gen. 36 8983
100. Ódor G 2003 Phase transition classes in triplet and quadruplet reaction-diffusion models Phys. Rev. E 67 056114
101. Ódor G 2004 Phase transitions of the binary production 2A → 3A, 4A → Ø model Phys. Rev. E 69 036112
102. Chaté H 2003 Private communication
103. Graham R L, Knuth D E and Patashnik O 1994 Concrete Mathematics (New York: Addison-Wesley)
104. Janssen H K, Schaub B and Schmittmann B 1989 New universal short-time scaling behaviour of critical relaxation processes Z. Phys. B 73 539