The Abelian Manna model on various lattices in one and two dimensions

Journal of Statistical Mechanics: Theory and Experiment

Volumn 2011, Issue 9, 2011, Pages

  Huynh, Hoai Nguyen ^a   Pruessner, Gunnar ^b   Chew, Lock Yue ^a  

^a NANYANG TECHNOLOGICAL UNIVERSITY   (Singapore)

^b IMPERIAL COLLEGE LONDON   (United Kingdom)

Author keywords

critical exponents and amplitudes (experiment); finite size scaling; sandpile models (experiment); self organized criticality (experiment)

Indexed keywords

EID: 80053486650     PISSN: None     EISSN: 17425468     Source Type: Journal    
DOI: 10.1088/1742-5468/2011/09/P09024     Document Type: Article

References (70)

1. Bak P, Tang C and Wiesenfeld K 1987 Phys. Rev. Lett. 59 381
2. Christensen K and Olami Z 1992 Phys. Rev. A 46 1829
3. Nakanishi H and Sneppen K 1997 Phys. Rev. E 55 4012
4. Ben-Hur A and Biham O 1996 Phys. Rev. E 53 R1317
5. Dhar D 2006 Proc. 11th Int. Summerschool on 'Fundamental Problems in Statistical Physics' (Leuven, Sept. 2005) Physica A 369 29
6. Duarte J A M S 1990 Cited in [69] as private communication for studying the BTW model on a triangular lattice
7. Manna S S 1991 Physica A 179 249
8. Hu C-K and Lin C-Y 2003 Physica A 318 92
9. Azimi-Tafreshi N, Dashti-Naserabadi H, Moghimi-Araghi S and Ruelle P 2010 J. Stat. Mech. P02004
10. Huynh H N, Chew L Y and Pruessner G 2010 Phys. Rev. E 82 042103
11. Manna S S 1991 J. Phys. A: Math. Gen. 24 L363
12. Syzi I 1951 Prog. Theor. Phys. 6 306
13. Itzykson C and Drouffe J-M 1997 Statistical Field Theory vol 1 1st edn (Cambridge: Cambridge University Press)
14. Dhar D 1999 Proc. 20th IUPAP Int. Conf. on Statistical Physics (Paris, July 1998) Physica A 263 4
15. Christensen K, Corral, Frette V, Feder J and Jssang T 1996 Phys. Rev. Lett. 77 107
16. Pruessner G and Jensen H J 2002 Phys. Rev. E 65 056707
17. Grassberger P 2002 New J. Phys. 4 17
18. Dorn P L, Hughes D S and Christensen K 2001 preprint from www.cmth.ph.ic.ac.uk/kim/papers/preprints/preprint-btw.pdf accessed 19 Oct. 2010
19. Olami Z, Feder H J S and Christensen K 1992 Phys. Rev. Lett. 68 1244
20. Dickman R and Campelo J M M 2003 Phys. Rev. E 67 066111
21. Dhar D 1999 overlaps with [14], updated in [5], arXiv:cond-mat/9909009
22. Liggett T M 2005 Stochastic Interacting Systems: Contact, Voter and Exclusion Processes (Berlin: Springer)
23. Hohenberg P C and Halperin B I 1977 Rev. Mod. Phys. 49 435
24. Paczuski M and Bassler K E 2000 according to [25], this is probably the correct version of [70] arXiv:cond-mat/0005340v2
25. Hughes D and Paczuski M 2002 Phys. Rev. Lett. 88 054302
26. Grnbaum B and Shephard G C 1987 Tilings and Patterns (New York, NY: Freeman)
27. Syzi I 1972 Phase Transitions and Critical Phenomena vol 2 ed C Domb and M S Green (London: Academic) pp 269-329
28. Baxter R J 2007 Exactly Solved Models in Statistical Mechanics (New York: Dover)
29. Loebl M 2010 Discrete Mathematics in Statistical Physics (Wiesbaden: Vieweg + Teubner)
30. Paczuski M and Boettcher S 1996 Phys. Rev. Lett. 77 111
31. Pruessner G 2004 J. Phys. A: Math. Gen. 37 7455
32. Morand J, Pruessner G and Christensen K 2010 unpublished
33. Efron B 1982 The Jackknife, the Bootstrap and Other Resampling Plans (Philadelphia, PA: SIAM)
34. Matsumoto M and Nishimura T 1998 ACM Trans. Model. Comput. Simul. 8 3
35. Marsaglia G Mersenne twister newsgroup posting 14 Jul 2005, 12:04am, accessed 10 May 2011 http://groups.google.com/group/sci.crypt/browse-thread/ thread/305c507efbe85be4
36. Marsaglia G Random numbers for c: The end? newsgroup posting 20 Jan 1999, 9:00am, accessed 10 May 2011 https://groups.google.com/group/sci.math.num- analysis/msg/eb4ddde782b17051
37. Brandt S 1998 Data Analysis (Berlin: Springer)
38. Pruessner G and Moloney N R 2003 J. Phys. A: Math. Gen. 36 11213
39. Lbeck S 2000 Phys. Rev. E 61 204
40. De Menech M, Stella A L and Tebaldi C 1998 Phys. Rev. E 58 R2677
41. Christensen K, Farid N, Pruessner G and Stapleton M 2008 Eur. Phys. J. B 62 331
42. Chessa A, Stanley H E, Vespignani A and Zapperi S 1999 Phys. Rev. E 59 R12
43. Pruessner G and Jensen H J 2004 Phys. Rev. E 70 066707
44. Jensen H J, Christensen K and Fogedby H C 1989 Phys. Rev. B 40 7425
45. Christensen K, Fogedby H C and Jensen H J 1991 J. Stat. Phys. 63 653
46. Christensen K and Olami Z 1993 Phys. Rev. E 48 3361
47. Wegner F J 1972 Phys. Rev. B 5 4529
48. Press W H, Teukolsky S A, Vetterling W T and Flannery B P 1992 Numerical Recipes in C 2nd edn (New York, NY: Cambridge University Press)
49. Binder K 1981 Z. Phys. B 43 119
50. Binder K 1981 Phys. Rev. Lett. 47 693
51. Privman V, Hohenberg P C and Aharony A 1991 Phase Transitions and Critical Phenomena vol 14 ed C Domb and J L Lebowitz (New York, NY: Academic) chapter 1 pp 1-134
52. Vespignani A and Zapperi S 1997 Phys. Rev. Lett. 78 4793
53. Dickman R, Vespignani A and Zapperi S 1998 Phys. Rev. E 57 5095
54. Lbeck S 2004 Int. J. Mod. Phys. B 18 3977
55. Christensen K 2004 Proc. Symp. Complexity and Criticality: in memory of Per Bak (1947-2002) (Copenhagen, Aug. 2003) Physica A 340 527
56. Pruessner G 2004 PhD Thesis Imperial College London, 180 Queen's Gate, London SW7 2BZ, UK accessed 19 Nov 2009 www.ma.imperial.ac.uk/ ∼ pruess/publications/thesis-final/
57. Bonachela J A 2008 PhD Thesis Departmento de Electromagnetismo y Fisca de la Materia & Institute Carlos I for Theoretical and Computational Physics, University of Granada, Granada accessed 12 Sept. 2009 http://hera.ugr.es/ tesisugr/17706312.pdf
58. Lbeck S and Heger P C 2003 Phys. Rev. E 68 056102
59. Jensen I 1999 J. Phys. A: Math. Gen. 32 5233
60. Chessa A, Vespignani A and Zapperi S 1999 Proc. Europhysics Conf. on Computational Physics CCP 1998 (Granada, Spain, Sept. 1998) Comput. Phys. Commun. 121/122 299
61. Voigt C A and Ziff R M 1997 Phys. Rev. E 56 R6241
62. Vespignani A, Dickman R, Muoz M A and Zapperi S 2000 Phys. Rev. E 62 4564
63. Bonachela J A and Muoz M A 2007 Proc. Int. Conf. on Statistical Physics (Raichak and Kolkata, Jan. 2007) Physica A 384 89 ISSN 0378-4371
64. Bonachela J A and Muoz M A 2008 Phys. Rev. E 78 041102
65. Marro J and Dickman R 1999 Nonequilibrium Phase Transitions in Lattice Models (New York, NY: Cambridge University Press)
66. Pruessner G 2007 Phys. Rev. E 76 061103
67. Pruessner G 2008 New J. Phys. 10 113003
68. Dhar D and Ramaswamy R 1989 Phys. Rev. Lett. 63 1659
69. Manna S S 1990 J. Stat. Phys. 59 509
70. Paczuski M and Bassler K E 2000 Phys. Rev. E 62 5347 according to [25], this (?) version 'was published by mistake. The correct version is arXiv:cond-mat/0005340'. This probably means arXiv:cond-mat/0005340v2