The effect of quenched disorder in neutral theories

Journal of Statistical Mechanics: Theory and Experiment

Volumn 2013, Issue 4, 2013, Pages

  Borile, Claudio ^a   Maritan, Amos ^a   Muñoz, Miguel A ^b  

^a UNIVERSITY OF PADOVA   (Italy)

^b UNIVERSITY OF GRANADA   (Spain)

Author keywords

disordered systems (theory); phase transitions into absorbing states (theory); stochastic particle dynamics (theory); stochastic processes

Indexed keywords

EID: 84876899972     PISSN: None     EISSN: 17425468     Source Type: Journal    
DOI: 10.1088/1742-5468/2013/04/P04032     Document Type: Article

References (55)

1. Zwanzig R 2001 Nonequilibrium Statistical Mechanics (New York: Oxford University Press)
2. Liggett T M 2004 Interacting particle systems Classics in Mathematics (Berlin: Springer)
3. Marro J and Dickman R 2005 Nonequilibrium phase transitions in lattice models Collection Aléa-Saclay (Cambridge: Cambridge University Press)
4. Henkel M, Hinrichsen H and Lübeck S 2008 Non-equilibrium phase transitions: absorbing phase transitions Theoretical and Mathematical Physics (London: Springer)
5. Ódor G 2008 Universality in Nonequilibrium Lattice Systems: Theoretical Foundations (Singapore: World Scientific)
6. Kimura M and Ohta T 1969 The average number of generations until fixation of a mutant gene in a finite population Genetics 61 763-71
7. Crow J F and Kimura M 2009 An Introduction to Population Genetics Theory (New Jersey: Blackburn Press)
8. Clifford P and Sudbury A 1973 A model for spatial conflict Biometrika 60 581-8
9. Pinto O A and Muñoz M A 2011 Quasi neutral theory of epidemic outbreaks Plos One 6 e21946
10. Liggett T M 2010 Continuous Time Markov Processes: An Introduction (Graduate Studies in Mathematics Series) (Providence, RI: American Mathematical Society)
11. Blythe R A and McKane A J 2007 Stochastic models of evolution in genetics, ecology and linguistics J. Stat. Mech. P07018
12. Hubbell S P 2008 The Unified Neutral Theory of Biodiversity and Biogeography (MPB-32) (Monographs in Population Biology) (Princeton, NJ: Princeton University Press)
13. Durrett R and Levin S A 1994 Stochastic spatial models: a user's guide to ecological applications Phil. Trans. R. Soc. B 343 329-50
14. Castellano C, Fortunato S and Loreto V 2009 Statistical physics of social dynamics Rev. Mod. Phys. 81 591-646
15. Croft W 2002 The Darwinization of linguistics Selection 3 75-91
16. Croft W 2006 The Relevance of an Evolutionary Model to Historical Linguistics (Amsterdam Studies in the Theory and History of Linguistic Science Series 4) vol 279 (Amsterdam: J Benjamins) p 91
17. Dornic I, Chaté H, Chave J and Hinrichsen H 2001 Critical coarsening without surface tension: the universality class of the voter model Phys. Rev. Lett. 87 045701
18. Al Hammal O, Chaté H, Dornic I and Muñoz M A 2005 Langevin description of critical phenomena with two symmetric absorbing states Phys. Rev. Lett. 94 230601
19. Krapivsky P L, Redner S and Ben-Naim E 2010 A Kinetic View of Statistical Physics (Cambridge: Cambridge University Press)
20. Molofsky J, Durrett R, Dushoff J, Griffeath D and Levin S 1999 Local frequency dependence and global coexistence Theoret. Populat. Biol. 55 270-82
21. Neuhauser C and Pacala S W 1999 An explicitly spatial version of the Lotka-Volterra model with interspecific competition Ann. Appl. Probab. 9 1226-59
22. Chesson P 2000 Mechanisms of maintenance of species diversity Annu. Rev. Ecol. Systemat. 31 343-66
23. Schweitzer F and Behera L 2009 Nonlinear voter models: the transition from invasion to coexistence Eur. Phys. J. B 67 301-18
24. Sturm A and Swart J 2008 Voter models with heterozygosity selection Ann. Appl. Probab. 18 59-99
25. Castellano C, Muñoz M A and Pastor-Satorras R 2009 Nonlinear q-voter model Phys. Rev. E 80 041129
26. Lee M Y and Vojta T 2010 Phase transitions of the generalized contact process with two absorbing states Phys. Rev. E 81 061128
27. Canet L, Chaté H, Delamotte B, Dornic I and Muñoz M A 2005 Nonperturbative fixed point in a nonequilibrium phase transition Phys. Rev. Lett. 95 100601
28. Peliti L 1986 Renormalisation of fluctuation effects in the A+A to A reaction J. Phys. A: Math. Gen. 19 L365
29. Harris A B and Lubensky T C 1974 Renormalization-group approach to the critical behavior of random-spin models Phys. Rev. Lett. 33 1540-3
30. Grinstein G and Luther A 1976 Application of the renormalization group to phase transitions in disordered systems Phys. Rev. B 13 1329-43
31. Imry Y and Wortis M 1979 Influence of quenched impurities on first-order phase transitions Phys. Rev. B 19 3580-5
32. Berker A N 1993 Critical behavior induced by quenched disorder Physica A 194 72-6
33. Moreira A G and Dickman R 1996 Critical dynamics of the contact process with quenched disorder Phys. Rev. E 54 R3090-3
34. Cafiero R, Gabrielli A and Muñoz M A 1998 Disordered one-dimensional contact process Phys. Rev. E 57 5060
35. Hooyberghs J, Iglói F and Vanderzande C 2003 Strong disorder fixed point in absorbing-state phase transitions Phys. Rev. Lett. 90 100601
36. Ódor G and Menyhárd N 2006 Critical behavior of an even-offspringed branching and annihilating random-walk cellular automaton with spatial disorder Phys. Rev. E 73 036130
37. Frachebourg L, Krapivsky P L and Redner S 1995 Heterogeneous catalysis on a disordered surface Phys. Rev. Lett. 75 2891-4
38. Masuda N, Gibert N and Redner S 2010 Heterogeneous voter models Phys. Rev. E 82 010103
39. Masuda N and Redner S 2011 Can partisan voting lead to truth? J. Stat. Mech. L02002
40. Mobilia M, Petersen A and Redner S 2007 On the role of zealotry in the voter model J. Stat. Mech. P08029
41. Pigolotti S and Cencini M 2010 Coexistence and invasibility in a two-species competition model with habitat-preference J. Theor. Biol. 265 609-17
42. Barghathi H and Vojta T 2012 Random fields at a nonequilibrium phase transition Phys. Rev. Lett. 109 170603
43. Imry Y and Ma S 1975 Random-field instability of the ordered state of continuous symmetry Phys. Rev. Lett. 35 1399-401
44. Gardiner C W 2002 Handbook of Stochastic Methods: for Physics, Chemistry and the Natural Sciences (Springer Series in Synergetics vol 13) (Berlin: Springer)
45. Graham R and Tél T 1985 Weak-noise limit of Fokker-Planck models and nondifferentiable potentials for dissipative dynamical systems Phys. Rev. A 31 1109
46. Graham R and Tél T 1986 Nonequilibrium potential for coexisting attractors Phys. Rev. A 33 1322-37
47. Ohtsuki H, Hauert C, Lieberman E and Nowak M A 2006 A simple rule for the evolution of cooperation on graphs and social networks Nature 441 502-5
48. Muñoz M A 1998 Nature of different types of absorbing states Phys. Rev. E 57 1377
49. Baxter G J, Blythe R A and McKane A J 2007 Exact solution of the multi-allelic diffusion model Math. Biosci. 209 124-70
50. Russell D I and Blythe R A 2011 Noise-induced dynamical transition in systems with symmetric absorbing states Phys. Rev. Lett. 106 165702
51. Gillespie D T 1977 Exact stochastic simulation of coupled chemical reactions J. Phys. Chem. 81 2340-61
52. Borile C, Muñoz M A, Azaele S, Banavar J R and Maritan A 2012 Spontaneously broken neutral symmetry in an ecological system Phys. Rev. Lett. 109 038102
53. Aizenman M and Wehr J 1989 Rounding of first-order phase transitions in systems with quenched disorder Phys. Rev. Lett. 62 2503-6
54. Kimura M and Takahata N 1995 Population Genetics, Molecular Evolution, and the Neutral Theory: Selected Papers, Evolutionary Biology (Chicage, IL: University of Chicago Press)
55. Kingman J F C 1982 The coalescent Stochastic Process. Appl. 13 235-48