[Aspects géométriques des phénomènes d'ordre]
Si un système macroscopique préparé dans une phase désordonnée est refroidi brusquement à une température inférieure à celle où, à l'équilibre, il y a une transition du second ordre, il subit alors un processus de coarsening au cours duquel il prend localement l'une des structures ordonnées stables à l'équilibre. L'étude de l'évolution de la morphologie des structures ordonnées en deux dimensions a récemment révélé deux propriétés génériques intéressantes. D'une part, la dynamique approche d'abord un état critique de percolation grâce à la croissance d'une nouvelle échelle de longueur, et vérifie des relations d'échelle vis-à-vis de celle-ci. Le temps nécessaire pour rejoindre l'état critique de percolation diverge avec la taille du système, moins faiblement que le temps nécessaire pour atteindre l'équilibre. D'autre part, après avoir atteint l'état critique de percolation, les propriétés géométriques et statistiques aux échelles plus longues que la longueur dynamique de croissance habituelle demeurent celles de la percolation critique. Ces observations sont communes aux différents types microscopiques de dynamique (retournement de spin simple, échange de spin local ou non, électeur) dans les systèmes purs ou faiblement désordonnés. On discute ces résultats et on renvoie aux publications originales pour davantage de détails.
A macroscopic system prepared in a disordered phase and quenched across a second-order phase transition into an ordered phase undergoes a coarsening process whereby it orders locally in one of the equilibrium states. The study of the evolution of the morphology of the ordered structures in two dimensions has recently unveiled two interesting and generic features. On the one hand, the dynamics first approach a critical percolating state via the growth of a new lengthscale and satisfying scaling properties with respect to it. The time needed to reach the critical percolating state diverges with the system size, though more weakly than the equilibration time. On the other hand, once the critical percolating structures established, the geometrical and statistical properties at larger scales than the one established by the usual dynamic growing length remain the ones of critical percolation. These observations are common to different microscopic dynamics (single spin flip, local and non-local spin exchange, voter) in pure or weakly disordered systems. We discuss these results and we refer to the relevant publications for details.
@article{CRPHYS_2017__18_1_5_0,
author = {Leticia F. Cugliandolo},
title = {Geometric aspects of ordering phenomena},
journal = {Comptes Rendus. Physique},
pages = {5--18},
publisher = {Elsevier},
volume = {18},
number = {1},
year = {2017},
doi = {10.1016/j.crhy.2016.10.002},
language = {en},
}
Leticia F. Cugliandolo. Geometric aspects of ordering phenomena. Comptes Rendus. Physique, Volume 18 (2017) no. 1, pp. 5-18. doi : 10.1016/j.crhy.2016.10.002. https://comptes-rendus.academie-sciences.fr/physique/articles/10.1016/j.crhy.2016.10.002/
[1] Adv. Phys., 43 (1994), p. 357
[2] Phase Transition Dynamics, Cambridge University Press, Cambridge, UK, 2004
[3] Kinetics of Phase Transitions (S. Puri; V. Wadhawan, eds.), Taylor and Francis Group, 2009
[4] Non-equilibrium Phase Transitions: Ageing and Dynamical Scaling Far from Equilibrium, Springer-Verlag, 2010
[5] A Kinetic View of Statistical Physics, Cambridge University Press, Cambridge, UK, 2010
[6] C. R. Physique, 16 (2015), p. 255
[7] J. Phys. A, 38 (2005)
[8] J. Stat. Mech. (2007)
[9] J. Stat. Phys., 36 (1984), p. 881
[10] Phys. Rep., 323 (2000), p. 81
[11] Ann. Phys., 318 (2005), p. 81
[12] Conformal random geometry (A. Bovier; F. Dunlop; F. den Hollander; A. van Enter; J. Dalibard, eds.), Mathematical Statistical Physics, Les Houches, vol. LXXXIII, Elsevier, France, 2006
[13] Some recent aspects of random conformally invariant systems (A. Bovier; F. Dunlop; F. den Hollander; A. van Enter; J. Dalibard, eds.), Mathematical Statistical Physics, Les Houches, vol. LXXXIII, Elsevier, 2006
[14] J. Phys. Chem. Solids, 19 (1961), p. 35
[15] Z. Elektrochem., 65 (1961), p. 581
[16] Grain Growth in Polycrystalline Materials (G. Abbruzzese; P. Brosso, eds.), Trans Tech Publications, Brookfield, VT, 1992
[17] Phys. Rev. A, 41 (1990), p. 1952
[18] Rep. Prog. Phys., 56 (1993), p. 733
[19] Contemp. Phys., 50 (2009), p. 199
[20] On Cellular Automaton Approaches to Modeling Biological Cells, Springer-Verlag, New York, 2002
[21] J. Phys. D, Appl. Phys., 23 (1990), p. 600
[22] J. Phys. C, 25 (2013), p. 404210
[23] J. Chem. Phys., 28 (1958), p. 258
[24] Phys. Rev. B, 34 (1986), p. 7845
[25] J. Stat. Mech. (2013)
[26] Interacting Particle Systems, Springer, New York, 1985
[27] J. Phys. B, 35 (2002), p. 1555
[28] J. Phys. B, 36 (2003), p. 4731
[29] J. Am. Chem. Soc., 63 (1941), p. 3083
[30] Scaling Concepts in Polymer Physics, Cornell University Press, Ithaca, NY, USA, 1979
[31] Introduction to Percolation Theory, Taylor and Francis, London, 1994
[32] Phys. Rep., 578 (2015), p. 1
[33] Phys. Rev. B, 16 (1977), p. 1426
[34] Phys. Rev. B, 48 (1993), p. 7221
[35] T. Blanchard, L.F. Cugliandolo, M. Picco, A. Tartaglia, Critical percolation in bidimensional kinetic spin models, (2016), in preparation.
[36] J. Phys. A, Math. Gen., 9 (1976), p. 2131
[37] J. Phys. A, Math. Gen., 13 (1980), p. 2775
[38] Phys. Lett. A, 50 (1974), p. 27
[39] J. Stat. Phys., 110 (2003), p. 1
[40] Phys. Rev. E, 76 (2007)
[41] J. Stat. Phys., 75 (1994), p. 1167
[42] J. Phys. A, Math. Gen., 29 (1996), p. 363
[43] Phys. Rev. Lett., 109 (2012)
[44] Acta Metall., 27 (1979), p. 1085
[45] Comput. Phys. Commun., 183 (2012), p. 1578
[46] Phys. Rev. E, 53 (1996)
[47] Phys. Rev. B, 38 (1988), p. 373
[48] Phys. Rev. B, 82 (2010)
[49] Phys. Rev. E, 84 (2011)
[50] Phys. Rev. B, 80 (2009)
[51] Growing length scales in aging systems (L. Berthier; J.-P. Bouchaud; G. Biroli; L. Cipelletti; W. van Saarloos, eds.), Dynamical Heterogeneities in Glasses, Colloids, and Granular Media, Oxford University Press, 2011
[52] Phys. Rev. Lett., 98 (2007)
[53] Europhys. Lett., 106 (2014), p. 66001
[54] Phys. Rev. E, 80 (2009)
[55] Phys. Rev. A, 92 (2015)
[56] Phase separation and critical percolation in bidimensional spin-exchange models, Europhys. Lett. (2016) (submitted for publication) | arXiv
[57] Phys. Rev. E, 92 (2015)
[58] Phys. Rev. E, 81 (2010)
[59] Phys. Rev. E, 85 (2012)
[60] F. Insalata, F. Corberi, L.F. Cugliandolo, M. Picco, Coarsening and percolation in a disordered ferromagnet, (2016), in preparation.
[61] J. Phys. A, 24 (1991)
[62] Physica A, 229 (1996), p. 72
[63] J. Stat. Mech. (2008)
[64] Phys. Rev. E, 85 (2012)
[65] Eur. Phys. J. B, 88 (2015), p. 160
[66] Z. Phys. B, 24 (1976), p. 113
[67] Z. Phys. B, 73 (1989), p. 539
[68] Phys. Rev. Lett., 76 (1996), p. 4589
[69] J. Stat. Mech. (2012)
[70] Europhys. Lett., 82 (2008), p. 10001
[71] et al. Phys. Rev. Lett., 101 (2008)
[72] Phys. Rev. E, 54 (1996), p. 2513
[73] Phys. Rev. E, 56 (1997), p. 3788
[74] Phys. Rev. E, 76 (2007)
[75] Exact results and open questions in first principle functional RG | arXiv
[76] Phys. Rev. Lett., 112 (2014)
[77] Phys. Rev. B, 76 (2007)
[78] Acta Mater., 88 (2015), p. 334
[79] Metal Interfaces, Americal Society for Metals, Cleveland, OH, USA, 1952, p. 108 (written discussion)
[80] Phys. Rep., 624 (2016), p. 1
[81] Phys. Rev. E, 86 (2012)
[82] Phys. Rev. E, 87 (2013)
[83] Phys. Rev. E, 63 (2001)
[84] Phys. Rev. E, 65 (2002)
[85] Phys. Rev. E, 80 (2009)
[86] Phys. Rev. E, 83 (2011)
[87] Phys. Rev. E, 88 (2013)
[88] J. Phys. A, 25 (1992)
[89] Phys. Lett. B, 541 (2002), p. 384
[90] Phys. Rev. E, 83 (2011)
[91] H. Ricateau, L.F. Cugliandolo, M. Picco, (2016), in preparation.
[92] Phys. Rev. Lett., 96 (2006)
[93] J. Stat. Phys., 130 (2008), p. 83
[94] J. Stat. Mech. (2009)
[95] et al. New J. Phys., 14 (2012)
[96] Europhys. Lett., 97 (2012), p. 30002
[97] J. Stat. Mech. Theory Exp., 2015 (2015)
[98] C. Godrèche, M. Picco, M. Pleimling, (2016), in preparation.
[99] Kinetics of Aggregation and Gelation, North Holland, Amsterdam, 1984
[100] Aggregation and Fractal Aggregates, World Scientific, Singapore, 1987
[101] Fractal Growth Phenomena, World Scientific, Singapore, 1989
[102] Phys. Rev. E, 53 (1996), p. 1789
[103] Phys. Rev. Lett., 95 (2005)
[104] J. Phys., Condens. Matter., 12 (2000), p. 8035
[105] Phys. Rev. E, 89 (2014)
[106] Phys. Rev. Lett., 112 (2014)
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