Abstract
The profile of interfaces separating different phases of statistical systems is investigated in the framework of renormalized field theory. The profile function is calculated analytically in the local potential approximation, using the effective potential to two loops. It can be interpreted as an intrinsic interfacial profile. The loop corrections to the leading tanh-type term turn out to be small. They yield a broadening of the interface.
Similar content being viewed by others
References
Widom, B.: In: Domb, C., Green, M. (eds.) Phase Transitions and Critical Phenomena, vol. 2. Academic Press, New York (1972)
Rowlinson, J., Widom, S.: Molecular Theory of Capillarity. Clarendon, Oxford (1982)
Binder, K.: Critical behavior at surfaces. In: Domb, C., Lebowitz, J. (eds.) Phase Transitions and Critical Phenomena, vol. 8. Academic Press, New York (1983)
Jasnow, D.: Critical phenomena at interfaces. Rep. Prog. Phys. 47, 1059–1132 (1984)
Safran, S.A.: Statistical Thermodynamics of Surfaces, Interfaces, and Membranes. Addison–Wesley, Reading (1994)
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)
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)
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)
Langevin, D. (ed.): Light Scattering by Liquid Surfaces and Complementary Techniques. Dekker, New York (1992)
Thomas, R.K.: Neutron reflection from liquid interfaces. Ann. Rev. Phys. Chem. 55, 91–426 (2004)
Stauffer, D.: Oil-water interfaces in the Ising-model. Prog. Colloid Polym. Sci. 103, 60–66 (1997)
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)
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)
Dünweg, B., Landau, D.P., Milchev, A. (eds.): Computer Simulations of Surfaces and Interfaces. Kluwer Academic, Dordrecht (2003)
Müller, M., Münster, G.: Profile and width of rough interfaces. J. Stat. Phys. 118, 669–686 (2005)
van der Waals, J.: The thermodynamic theory of capillarity under the hypothesis of a continuous variation of density. Verhandel Konink. Akad. Weten. 1, (1893). English translation: J. Rowlinson, J. Stat. Phys. 20, 97–244 (1979)
Le Bellac, M.: Quantum and Statistical Field Theory. Clarendon, Oxford (1991)
Cahn, J., Hilliard, J.: Free energy of a nonuniform system. J. Chem. Phys. 28, 258–267 (1958)
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)
Buff, F., Lovett, R., Stillinger, F.: Interfacial density profile for fluids in the critical region. Phys. Rev. Lett. 15, 621–623 (1965)
Weeks, J.: Structure and thermodynamics of the liquid–vapor interface. J. Chem. Phys. 67, 3106–3121 (1977)
Parisi, G.: Field-theoretic approach to second-order phase transition in two-and three-dimensional systems. J. Stat. Phys. 23, 49–82 (1980)
Le Guillou, J.C., Zinn-Justin, J.: Critical exponents from field theory. Phys. Rev. B 21, 3976–3998 (1980)
Münster, G.: Interface tension in three-dimensional systems from field theory. Nucl. Phys. B 340, 559–567 (1990)
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)
Gutsfeld, C., Küster, J., Münster, G.: Calculation of universal amplitude ratios in three-loop order. Nucl. Phys. B 479, 654–662 (1996)
Küster, J.: Kritisches Verhalten fluktuierender Grenzflächen. PhD thesis, Univ. of Münster (2001)
Ohta, T., Kawasaki, K.: Renormalization group approach to the interfacial order parameter profile near the critical point. Prog. Theor. Phys. 58, 467–481 (1977)
Rudnick, J., Jasnow, D.: ε expansion for the interfacial profile. Phys. Rev. B 17, 1351–1354 (1978)
Jasnow, D., Rudnick, J.: Interfacial profile in three dimensions. Phys. Rev. Lett. 41, 698–701 (1978)
Sikkenk, J.H., van Leeuwen, J.M.J.: ε-expansion for the interfacial profile in an external field. Physica A 137, 156–177 (1986)
Jackiw, R.: Functional evaluation of the effective potential. Phys. Rev. D 9, 1686–1701 (1974)
Iliopoulos, J., Itzykson, C., Martin, A.: Functional methods and perturbation theory. Rev. Mod. Phys. 47, 165–192 (1975)
Amit, D.J.: Field Theory, the Renormalization Group and Critical Phenomena. McGraw–Hill, New York (1978)
Coleman, S., Weinberg, E.: Radiative corrections as the origin of spontaneous symmetry breaking. Phys. Rev. D 7, 1888–1910 (1973)
Weinberg, E.J., Wu, A.: Understanding complex perturbative effective potentials. Phys. Rev. D 36, 2474–2480 (1987)
Sher, M.: Electroweak Higgs potentials and vacuum stability. Phys. Rep. 179, 273–418 (1989)
Meyer-Ortmanns, H., Reisz, T.: Principles of Phase Structures in Particle Physics. World Scientific, Singapore (2007)
Symanzik, K.: Renormalizable models with simple symmetry breaking, I: symmetry breaking by a source term. Commun. Math. Phys. 16, 48–80 (1970)
Langer, J.S.: Statistical theory of the decay of metastable states. Ann. Phys. 54, 258–275 (1969)
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)
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)
Lüscher, M., Weisz, P.: Scaling laws and triviality bounds in the lattice φ 4-theory; one-component model in the phase with spontaneous broken symmetry. Nucl. Phys. B 295, 65–92 (1987)
Caselle, M., Hasenbusch, M.: Universal amplitude ratios in the 3D Ising model. J. Phys. A 30, 4963–4982 (1997)
Liu, A.J., Fisher, M.E.: The three-dimensional Ising model revisited numerically. Physica A 156, 35–76 (1989)
Guida, R., Zinn-Justin, J.: Critical exponents of the N-vector model. J. Phys. A 31, 8103–8121 (1998)
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)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Küster, J., Münster, G. The Interfacial Profile in Two-Loop Order. J Stat Phys 129, 441–451 (2007). https://doi.org/10.1007/s10955-007-9404-z
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10955-007-9404-z