The interfacial profile in two-loop order

Journal of Statistical Physics

Volumn 129, Issue 3, 2007, Pages 441-451

  Küster, Jens ^a   Münster, Gernot ^a  

^a UNIVERSITY OF MÜNSTER   (Germany)

Author keywords

Field theory; Interfaces

Indexed keywords

EID: 35348916579     PISSN: 00224715     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10955-007-9404-z     Document Type: Article

References (48)

1. Widom, B.: In: Domb, C., Green, M. (eds.) Phase Transitions and Critical Phenomena, vol. 2. Academic Press, New York (1972)
2. Rowlinson, J., Widom, S.: Molecular Theory of Capillarity. Clarendon, Oxford (1982)
3. Binder, K.: Critical behavior at surfaces. In: Domb, C., Lebowitz, J. (eds.) Phase Transitions and Critical Phenomena, vol. 8. Academic Press, New York (1983)
4. Jasnow, D.: Critical phenomena at interfaces. Rep. Prog. Phys. 47, 1059-1132 (1984)
5. Safran, S.A.: Statistical Thermodynamics of Surfaces, Interfaces, and Membranes. Addison-Wesley, Reading (1994)
6. Binder, K.: Finite size effects in thin film simulations. In: Dünweg, B., Landau, D.P., Milchev, A. (eds.) Computer Simulations of Surfaces and Interfaces. Kluwer Academic, Dordrecht (2003)
7. Binder, K.: Simulations of interfaces between coexisting phases: multiscale aspects. In: Brandt, A., Bernholc, J., Binder, K. (eds.) Multiscale Simulations in Chemistry and Physics. IOS Press, Amsterdam (2001)
8. Huang, J.S., Webb, W.W.: Viscous damping of thermal excitations on the interface of critical fluid mixtures. Phys. Rev. Lett. 23, 160-163 (1969)
9. Langevin, D. (ed.): Light Scattering by Liquid Surfaces and Complementary Techniques. Dekker, New York (1992)
10. Thomas, R.K.: Neutron reflection from liquid interfaces. Ann. Rev. Phys. Chem. 55, 91-426 (2004)
11. Stauffer, D.: Oil-water interfaces in the Ising-model. Prog. Colloid Polym. Sci. 103, 60-66 (1997)
12. Werner, A., Schmid, F., Müller, M., Binder, K.: Anomalous size-dependence of interfacial profiles between coexisting phases of polymer mixtures in thin film geometry: a Monte-Carlo simulation. J. Chem. Phys. 107, 8175-8188 (1997)
13. Werner, A., Schmid, F., Müller, M., Binder, K.: " Intrinsic" profiles and capillary waves at homopolymer interfaces: a Monte Carlo study. Phys. Rev. E 59, 728-738 (1999)
14. Dünweg, B., Landau, D.P., Milchev, A. (eds.): Computer Simulations of Surfaces and Interfaces. Kluwer Academic, Dordrecht (2003)
15. Müller, M., Münster, G.: Profile and width of rough interfaces. J. Stat. Phys. 118, 669-686 (2005)
16. van der Waals, J.: The thermodynamic theory of capillarity under the hypothesis of a continuous variation of density. Verhandel Konink. Akad. Weten. 1, (1893).
17. English translation: J. Rowlinson, J. Stat. Phys. 20, 97-244 (1979)
18. Le Bellac, M.: Quantum and Statistical Field Theory. Clarendon, Oxford (1991)
19. Cahn, J., Hilliard, J.: Free energy of a nonuniform system. J. Chem. Phys. 28, 258-267 (1958)
20. Fisk, S., Widom, B.: Structure and free energy of the interface between fluid phases in equilibrium near the critical point. J. Chem. Phys. 50, 3219-3227 (1960)
21. Buff, F., Lovett, R., Stillinger, F.: Interfacial density profile for fluids in the critical region. Phys. Rev. Lett. 15, 621-623 (1965)
22. Weeks, J.: Structure and thermodynamics of the liquid-vapor interface. J. Chem. Phys. 67, 3106-3121 (1977)
23. Parisi, G.: Field-theoretic approach to second-order phase transition in two-and three-dimensional systems. J. Stat. Phys. 23, 49-82 (1980)
24. Le Guillou, J.C., Zinn-Justin, J.: Critical exponents from field theory. Phys. Rev. B 21, 3976-3998 (1980)
25. Münster, G.: Interface tension in three-dimensional systems from field theory. Nucl. Phys. B 340, 559-567 (1990)
26. Münster, G., Heitger, J.: Field-theoretic calculation of the universal amplitude ratio of correlation lengths in 3D Ising systems. Nucl. Phys. B 424, 582-594 (1994)
27. Gutsfeld, C., Küster, J., Münster, G.: Calculation of universal amplitude ratios in three-loop order. Nucl. Phys. B 479, 654-662 (1996)
28. Küster, J.: Kritisches Verhalten fluktuierender Grenzflächen. PhD thesis, Univ. of Münster (2001)
29. Ohta, T., Kawasaki, K.: Renormalization group approach to the interfacial order parameter profile near the critical point. Prog. Theor. Phys. 58, 467-481 (1977)
30. Rudnick, J., Jasnow, D.: ε expansion for the interfacial profile. Phys. Rev. B 17, 1351-1354 (1978)
31. Jasnow, D., Rudnick, J.: Interfacial profile in three dimensions. Phys. Rev. Lett. 41, 698-701 (1978)
32. Sikkenk, J.H., van Leeuwen, J.M.J.: ε-expansion for the interfacial profile in an external field. Physica A 137, 156-177 (1986)
33. Jackiw, R.: Functional evaluation of the effective potential. Phys. Rev. D 9, 1686-1701 (1974)
34. Iliopoulos, J., Itzykson, C., Martin, A.: Functional methods and perturbation theory. Rev. Mod. Phys. 47, 165-192 (1975)
35. Amit, D.J.: Field Theory, the Renormalization Group and Critical Phenomena. McGraw-Hill, New York (1978)
36. Coleman, S., Weinberg, E.: Radiative corrections as the origin of spontaneous symmetry breaking. Phys. Rev. D 7, 1888-1910 (1973)
37. Weinberg, E.J., Wu, A.: Understanding complex perturbative effective potentials. Phys. Rev. D 36, 2474-2480 (1987)
38. Sher, M.: Electroweak Higgs potentials and vacuum stability. Phys. Rep. 179, 273-418 (1989)
39. Meyer-Ortmanns, H., Reisz, T.: Principles of Phase Structures in Particle Physics. World Scientific, Singapore (2007)
40. Symanzik, K.: Renormalizable models with simple symmetry breaking, I: symmetry breaking by a source term. Commun. Math. Phys. 16, 48-80 (1970)
41. Langer, J.S.: Statistical theory of the decay of metastable states. Ann. Phys. 54, 258-275 (1969)
42. Münster, G., Rotsch, S.: Analytical calculation of the nucleation rate for first order phase transitions beyond the thin wall approximation. Eur. Phys. J. C 12, 161-171 (2000)
43. Binder, K.: Spinodal decomposition. In: Cahn, R.W., Haasen, P., Kramer, E.J. (eds.) Materials Science and Technology, vol. 5: Phase Transformations in Materials. Wiley-VCH, Weinheim (1991)
44. 4-theory; one-component model in the phase with spontaneous broken symmetry. Nucl. Phys. B 295, 65-92 (1987)
45. Caselle, M., Hasenbusch, M.: Universal amplitude ratios in the 3D Ising model. J. Phys. A 30, 4963-4982 (1997)
46. Liu, A.J., Fisher, M.E.: The three-dimensional Ising model revisited numerically. Physica A 156, 35-76 (1989)
47. Guida, R., Zinn-Justin, J.: Critical exponents of the N-vector model. J. Phys. A 31, 8103-8121 (1998)
48. Hasenbusch, M., Pinn, K., Vinti, S.: Critical exponents of the 3D Ising universality class from finite size scaling with standard and improved actions. Phys. Rev. B 59, 11471 (1999)