Abstract
The field theoretic renormalization-group approach for the study of critical behavior near free surfaces is generalized to dynamic properties. Time-dependent Ginzburg-Landau models with nonconserved or conserved order parameters — semi-infinite generalizations of the so-called modelsA andB — are considered. The asymptotic behavior of response and correlation functions is analyzed at the ordinary and special transitions in 4-ɛ dimensions, and dynamic scaling laws for surface quantities are obtained. It is shown that the critical exponents can be expressed entirely in terms of static bulk and surface exponents andz, the dynamic bulk exponent. The critical exponents for the leading frequency, temperature and momentum singularities of the surface two-spin correlation function at the ordinary transition differ appreciably from the corresponding bulk analogues. In addition, the shape function which describes its frequency dependence differs qualitatively from the one of the bulk correlation function.
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References
For background information and an extensive list of references see: Binder, K.: Critical behaviour at surfaces. In: Phase transitions and critical phenomena. Domb, C., Lebowitz, J.L. (eds.) Vol. 10. New York: Academic Press (to be published). A short summary of the field-theoretic work is given in [2]
Diehl, H.W.: J. Appl. Phys.53, 7914 (1982)
For a review on dynamic critical phenomena in the bulk see: Hohenberg, P.C., Halperin, B.I.: Rev. Mod. Phys.49, 435 (1977)
Bausch, R., Janssen, H.K., Wagner, H.: Z. Phys. B — Condensed Matter24, 113 (1976)
Dominicis, C. de, Peliti, L.: Phys. Rev. B18, 353 (1978)
Diehl, H.W., Dietrich, S.: Z. Phys. Lett.80A, 408 (1980)
Diehl, H.W., Dietrich, S.: Z. Phys. B — Condensed Matter42, 65 (1981)
Dietrich, S., Diehl, H.W.: Z. Phys. B — Condensed Matter43, 315 (1981)
Diehl, H.W., Dietrich, S.: Phys. Rev. B24, 2878 (1981)
Diehl, H.W., Dietrich, S.: Z. Phys. B — Condensed Matter50, 117 (1983)
Diehl, H.W., Eisenriegler, E.: Phys. Rev. Lett.48, 1767 (1982)
Diehl, H.W., Dietrich, S., Eisenriegler, E.: Phys. Rev. B27, 2937 (1983)
Halperin, B.I., Hohenberg, P.C., Ma, S.: Phys. Rev. Lett.29, 1548 (1972); Phys. Rev. B10, 139 (1974)
Martin, P.C., Siggia, E.D., Rose, H.A.: Phys. Rev. A8, 423 (1973)
Janssen, H.K.: Z. Phys. B — Condensed Matter23, 377 (1976)
Tanaka, F.: J. Phys. C12, 5535 (1979)
Suzuki, N.: Prog. Theor. Phys.58, 1142 (1977)
Yalabik, N.C., Gunton, J.D.: Prog. Theor. Phys.62, 1573 (1979)
Pesch, W., Mikeska, H.J.: Z. Phys. B — Condensed Matter30, 177 (1978)
Kumar, P.: Phys. Rev. B10, 2928 (1974)
Kumar, P., Maki, K.: Phys. Rev. B13, 2011 (1976)
Symanzik, K.: Nucl. Phys. B190 [FS3], 1 (1981)
Langouche, F., Roekaerts, D., Tirapegui, E.: Physica95A, 252 (1979)
Deker, U., Haake, F.: Phys. Rev. A11, 2043 (1975)
Wagner, H.: Acta Phys. Austriaca, Suppl. XVIII, 543 (1977)
Brézin, E., LeGuillou, J.C., Zinn-Justin, J.: In: Phase transitions and critical phenomena. Domb, C., Green, M.S. (eds.), Vol. 6. New York: Academic Press 1976
Amit, D.J.: Field theory, the renormalization group, and critical phenomena. New York: McGraw-Hill 1978
Gradsteyn, I.S., Rhyzik, I.M.: Table of integrals, series, and products. New York: Academic Press 1980
Gelfand, I.M., Shilov, G.E.: Generalized functions. Vol. 1. New York: Academic Press 1964
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Dietrich, S., Diehl, H.W. The effects of surfaces on dynamic critical behavior. Z. Physik B - Condensed Matter 51, 343–354 (1983). https://doi.org/10.1007/BF01319217
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DOI: https://doi.org/10.1007/BF01319217