Critical dynamics in thin films

Journal of Statistical Physics

Volumn 123, Issue 5, 2006, Pages 929-1005

  Gambassi, A ^a,b   Dietrich, S ^a,b  

^a MAX PLANCK INSTITUTE FOR INTELLIGENT SYSTEMS   (Germany)

^b UNIVERSITY OF STUTTGART   (Germany)

Author keywords

Confined geometry; Critical casimir force; Dynamic critical phenomena; Finite size scaling; Magnetic properties of films

Indexed keywords

EID: 33746946030     PISSN: 00224715     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10955-006-9089-8     Document Type: Article

References (94)

1. J. Zinn-Justin, Quantum Field Theory and Critical Phenomena, 3rd ed. (Clarendon, Oxford, 1996).
2. P. C. Hohenberg and B. I. Halperin, Theory of dynamic critical phenomena. Rev. Mod. Phys. 49:435 (1977).
3. A. Pelissetto and E. Vicari, Critical phenomena and renormalization-group theory. Phys. Rep. 368:549 (2002).
4. R. Folk and G. Moser, Critical dynamics in two loop order. Acta Phys. Slav. 52:285 (2002).
5. K. Binder, Critical Behaviour at Surfaces, in Phase Transition and Critical Phenomena. Edited by C. Domb and J. L. Lebowitz (Academic, London, 1983), Vol. 8, p. 2.
6. H. W. Diehl, Field-theoretical approach to critical behaviour at surfaces, in Phase Transition and Critical Phenomena. Edited by C. Domb and J. L. Lebowitz (Academic, London, 1986), Vol. 10, p. 75.
7. M. Pleimling, Critical phenomena at perfect and non-perfect surfaces. J. Phys. A: Math. Gen. 37:R79 (2004).
8. S. Dietrich and H. W. Diehl, The effects of surfaces on dynamic critical behavior. Z. Phys. B 51:343 (1983).
9. H. W. Diehl and H. K. Janssen, Boundary conditions for the field theory of dynamic critical behavior in semi-infinite systems with conserved order parameter. Phys. Rev. A 45:7145 (1992);
10. H. W. Diehl, Universality classes for the dynamic surface critical behavior of systems with relaxational dynamics. Phys. Rev. B 49:2846 (1994);
11. F. Wichmann and H. W. Diehl, Dynamic surface critical behavior of systems with conserved bulk order parameter: detailed RG analysis of the semi-infinite extensions of model B with and without nonconservative surface terms. Z. Phys. B 97:251 (1995).
12. M. N. Barber, Finite-size Scaling, in Phase Transition and Critical Phenomena. Edited by C. Domb and J. L. Lebowitz (Academic, London, 1983), Vol. 8, p. 145.
13. Finite-size Scaling, edited by J. L. Cardy (North-Holland, Amsterdam, 1988).
14. J. G. Brankov, D. M. Dantchev and N. S. Tonchev, The Theory of Critical Phenomena in Finite-Size Systems - Scaling and Quantum Effects (World Scientific, Singapore, 2000).
15. M. Krech and S. Dietrich, Free energy and specific heat of critical films and surfaces. Phys. Rev. A 46:1886 (1992).
16. M. Krech and S. Dietrich, The specific heat of critical films, the Casimir force, and wetting films near critical end points. Phys. Rev. A 46:1922 (1992).
17. M. Krech, The Casimir Effect in Critical Systems (World Scientific, Singapore, 1994).
18. F. Schlesener, A. Hanke and S. Dietrich, Critical Casimir forces in colloidal suspensions. J. Stat. Phys. 110:981 (2003).
19. R. Klimpel and S. Dietrich, Structure factor of thin films near continous phase transitions Phys. Rev. B 60:16977 (1999).
20. V. Dohm, The superfluid transition in confined 4He: Renormalization-group theory. Phys. Scripta 149:46 (1993).
21. A. Onuki, Phase transition dynamics (Cambridge University Press, Cambridge, 2002).
22. S. Puri, Surface-directed spinodal decomposition. J. Phys.: Condens. Matter 17:R101 (2005).
23. S. K. Das, S. Puri, J. Horbach and K. Binder, Kinetics of phase separation in thin films: Simulations for the diffusive case. e-print Phys. Rev. E 72, 061603 (2005).
24. Y. Y. Goldschmidt, Finite size scaling effects in dynamics, Nucl. Phys. B 280 [FS18], 340 (1987); reprinted in Ref.11.
25. J. C. Niel and J. Zinn-Justin, Finite size effects in critical dynamics. Nucl. Phys. B 280 [FS18], 355 (1987).
26. J. C. Niel, Critical dynamics, finite-size effects and supersymmetry. Phys. Rev. B 37:2156 (1988).
27. H. W. Diehl, Finite size effects in critical dynamics and the renormalization group. Z. Phys. B 66:211 (1987).
28. W. Koch, V. Dohm and D. Stauffer, Order-parameter relaxation times of finite three-dimensional Ising-like systems. Phys. Rev. Lett. 77:1789 (1996).
29. K. Oerding, Relaxation times in a finite Ising system with random impurities. J. Stat. Phys. 78:893 (1995).
30. U. Ritschel and H. W. Diehl, Long-time traces of the initial condition in relaxation phenomena near criticality. Phys. Rev. E 51:5392 (1995);
31. Dynamic relaxation and universal short-time behavior in finite systems: The renormalization-group approach. Nucl. Phys. B 464:512 (1996).
32. H. W. Diehl and U. Ritschel, Dynamical relaxation and universal short-time behavior of finite systems, J. Stat. Phys. 73:1 (1993).
33. W. Koch and V. Dohm, Finite-size effects on critical diffusion and relaxation towards metastable equilibrium. Phys. Rev. E 58:R1179 (1998).
34. M. Krech and D. P. Landau, Spin-dynamics simulations of the three-dimensional XY model: structure factor and transport properties. Phys. Rev. B 60:3375 (1999).
35. Z. -B. Li, U. Ritschel and B. Zheng, Monte Carlo simulation of universal short-time behavior in critical relaxation. J. Phys. A: Math. Gen. 27:L837 (1994).
36. K. Nho and E. Manousakis, Scaling of thermal conductivity of helium confined in pores. Phys. Rev. B 64:144513 (2001).
37. 4He near the superfluid transition in a restricted geometry. Phys. Rev. Lett. 74:944 (1995);
38. λ, Phys. Rev. Lett. 90:025301 (2003).
39. V. Dohm, Renormalization-group flow equations of model F. Phys. Rev. B 44:2697 (1991).
40. λ. Physica B 329-333:200 (2003).
41. λ. Phys. Rev. Lett. 62:1864 (1989);
42. λ. Physica B 165&166:543 (1990);
43. λ: renormalization-group theory. Z. Phys. B 84:443 (1991);
44. 4He in the presence of a heat current: renormalization-group theory. Physica B 197:215 (1994).
45. 4He and a solid surface. Phys. Rev. Lett. 88:095702 (2002).
46. J. K. Bhattacharjee, Critical diffusivity in restricted geometry: Decoupled mode approximation. Phys. Rev. Lett. 77:1524 (1996).
47. R. A. Ferrell, Decoupled-mode dynamical scaling theory of the binary-liquid phase transition. Phys. Rev. Lett. 24:1169 (1970).
48. M. Calvo and R. A. Ferrell, Critical diffusion in a bounded fluid. I, Phys. Rev. A 31:2570 (1985);
49. M. Calvo, Critical diffusion in a bounded fluid. II. Temperature- dependent effects. Phys. Rev. A 31:2588 (1985).
50. S. Battacharyya and J. K. Bhattacharjee, Critical ultrasonics near the superfluid transition: finite-size effects. J. Phys. A: Math. Gen. 31:L575 (1998);
51. Superfluid transition in a finite geometry: Critical ultrasonics. Phys. Rev. B 58:15146 (1998).
52. D. Bartolo, A. Ajdari and J.-B. Fournier, Effective interactions between inclusions in complex fluids driven out of equilibrium. Phys. Rev. E 67:061112 (2003).
53. A. Najafi and R. Golestanian, Forces induced by non-equilibrium fluctuations: The Soret-Casimir effect. e-print cond-mat/0308373v1 (2003).
54. Part of this work has been published in Europhys. Lett. 68:776 (2004).
55. E. Frey and F. Schwabl, Critical dynamics of magnets. Adv. Phys. 43:577 (1994).
56. H. Nakanishi and M. E. Fisher, Critical point shifts in films. J. Chem. Phys. 78:3279 (1983).
57. Y. Rouault, J. Baschnagel and K. Binder, Phase separation of symmetrical polymer mixtures in thin-film geometry. J. Stat. Phys. 80:1009 (1995).
58. D. O'Connor and C. R. Stephens, Renormalization group theory of crossovers. Phys. Rep. 363:425 (2002).
59. P. Calabrese, V. Martin-Mayor, A. Pelissetto and E. Vicari, Dynamic structure factor of the three-dimensional Ising model with purely relaxational dynamics. Phys. Rev. E 68:016110 (2003).
60. V. Privman, P. C. Hohenberg and A. Aharony, Universal critical-point amplitude ratios, in Phase Transition and Critical Phenomena. Edited by C. Domb and J. L. Lebowitz (Academic, New York, 1991), Vol. 14, p. 1.
61. H. K. Janssen, Lagrangean for classic field dynamics and renormalization group calculations of dynamical critical properties. Z. Phys. B 23:377 (1976);
62. R. Bausch, H. K. Janssen and H. Wagner, Renormalized field-theory of critical dynamics. Z. Phys. B 24:113 (1976).
63. F. Langouche, D. Roekaerts and E. Tirapegui, Functional integral methods for stochastic fields. Physica A 95:252 (1979).
64. M. Krech, E. Eisenriegler and S. Dietrich, Energy density profiles in critical films. Phys. Rev. E 52:1345 (1995).
65. G. Gompper and H. Wagner, Conformal invariance in semi-infinite systems: application to critical surface scattering. Z. Phys. B 59:193 (1985).
66. S. Dietrich, Static and dynamic critical phenomena at surfaces, in Magnetic Properties of Low-Dimensional Systems II, Edited by L. M. Falicov, F. Mejia-Lira, and J. L. Morán-López (Springer, Berlin, 1990), p. 150.
67. D. Dantchev and M. Krech, Critical Casimir force and its fluctuations in lattice spin models: Exact and Monte Carlo results. Phys. Rev. E 69:046119 (2004).
68. D. Bartolo, A. Ajdari, J.-B. Fournier and R. Golestanian, Fluctuations of fluctuation-induced Casimir-like forces. Phys. Rev. Lett. 89:230601 (2002).
69. M. J. Dunlavy and D. Venus, Critical slowing down in the two-dimensional Ising model measured using ferromagnetic ultrathin films. Phys. Rev. B 71:144406 (2005).
70. S. Dietrich and A. Haase, Scattering of X-rays and neutrons at interfaces. Phys. Rep. 260:1 (1995).
71. R. Bausch and H. K. Janssen, Equation of motion and nonlinear response near the critical point. Z. Phys. B 25:275 (1976).
72. R. Bausch, E. Eisenriegler and H. K. Janssen, Nonlinear critical slowing down of the one-component Ginzburg-Landau field. Z. Phys. B 36:179 (1979).
73. Z. Rácz, Nonlinear relaxation near the critical point: molecular-field and scaling theory. Phys. Rev. B 13:263 (1976).
74. M. E. Fisher and Z. Rácz, Scaling theory of nonlinear critical relaxation. Phys. Rev. B 13:5039 (1976).
75. H. Riecke, Nichtlineare Relaxation in halbunendlichen Systemen, diploma thesis, Ludwig-Maximilians-Universität, München (1982).
76. M. Kikuchi and Y. Okabe, Monte Carlo Study of Critical Relaxation near a Surface. Phys. Rev. Lett. 55:1220 (1985).
77. H. Riecke, S. Dietrich and H. Wagner, Field theory for nonlinear critical relaxation near a surface. Phys. Rev. Lett. 55:3010 (1985).
78. M. E. Fisher and H. Nakanishi, Scaling theory for the criticality of fluids between plates. J. Chem. Phys. 75:5857 (1981).
79. M. Krech, Casimir forces in binary liquid mixtures. Phys. Rev. E 56:1642 (1997).
80. A. P. Prudnikov, Yu. A. Brychkov and O. I. Marichev, Integrals and Series, Vol. 1: Elementary Functions (Gordon and Breach, New York, 1986).
81. Handbook of Mathematical Functions, edited by M. Abramowitz and I. A. Stegun (Dover, New York, 1970).
82. I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series, and Products (Academic, London, 1965).
83. M. I. Kaganov and A. N. Omel'yanchuk, Phenomenological theory of phase transition in a thin ferromagnetic plate. Sov. Phys. JETP 34:895 (1972);
84. Zh. Eksp. Teor. Fiz. 61, 1679 (1971).
85. M. I. Kaganov, Surface magnetism. Sov. Phys. JETP 35:631 (1972);
86. Zh. Eksp. Teor. Fiz. 62, 1196 (1972).
87. P. F. Byrd and M. D. Friedman. Handbook of Elliptic Integrals for Engineers and Scientist (Springer, Berlin, 1971).
88. P. Kumar, Magnetic phase transition at a surface: mean-field theory. Phys. Rev. B 10:2928 (1974).
89. T. C. Lubensky and M. H. Rubin, Critical phenomena in semi-infinite systems II: mean-field theory. Phys. Rev. B 12:3885 (1975).
90. H. K. Janssen, B. Schaub and B. Schmittmann, New universal short-time scaling behaviour of critical relaxation processes. Z. Phys B 73:539 (1989);
91. H. K. Janssen, On the renormalized field theory of nonlinear critical relaxation, in From Phase Transitions to Chaos- Topics in Modern Statistical Physics. Edited by G. Györgyi, I. Kondor, L. Sasvári and T. Tel (World Scientific, Singapore, 1992).
92. U. Ritschel and P. Czerner, Universal short-time behavior in critical dynamics near surfaces, Phys. Rev. Lett. 75:3882 (1995);
93. S. N. Majumdar and A. M. Sengupta, Nonequilibrium dynamics following a quench to the critical point in a semi-infinite system. Phys. Rev. Lett. 76:2394 (1996);
94. M. Pleimling and F. Iglói, Nonequilibrium critical dynamics at surfaces: cluster dissolution and nonalgebraic correlations. Phys. Rev. Lett. 92:145701 (2004).