Multicritical behaviour at surfaces
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Abstract
The critical behaviour of a semi-infiniten-vector model with a surface term (c/2) ∫dSφ2 is studied in 4-ε dimensions near the special transition. It is shown that all critical surface exponents derive from bulk exponents and η∥, the anomalous dimension of the order parameter at the surface. The surface exponents and the crossover exponent Φ for the variablec are calculated to second order in ε. It is found that Φ does not satisfy the relation Φ=1-ν predicted by Bray and Moore. The order-parameter profilem(z)=<ø> is calculated to first order in ε. In contrast to mean-field theory,m(z) is not flat nor does it satisfy a Neumann boundary condition. General aspects of the field-theoretic renormalization program for systems with surfaces are discussed with particular attention paid to the explanation of the unfamiliar new features caused by the presence of surfaces.
Keywords
Spectroscopy Boundary Condition Neural Network State Physics Complex SystemPreview
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References
- 1.Diehl, H.W., Dietrich, S.: Z. Phys. B — Condensed Matter42, 65 (1981); Phys. Lett.80A, 408 (1980)Google Scholar
- 2.Brézin, E., Le Guillou, J.C., Zinn-Justin, J.: In: Phase transitions and critical phenomena. Domb, C., Green, M.S. (eds.), Vol. 6. New York: Academic Press 1976Google Scholar
- 3.Amit, D.J.: Field theory, the renormalization group, and critical phenomena. New York: Mc Graw-Hill 1978Google Scholar
- 4.Diehl, H.W., Dietrich, S.: Phys. Rev. B24, 2878 (1981)Google Scholar
- 5.see eg.: Bjorken, J.D., Drell, S.D.: Relativistische Quantenfeldtheorie. BI Hochschultaschenbuch Nr. 101/101 a. Mannheim: Bibliographisches Institut 1966Google Scholar
- 6.Symanzik, K.: Nucl. Phys. B190 [FS3], 1 (1981)Google Scholar
- 7.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)Google Scholar
- 8.Diehl, H.W.: Critical behaviour of semi-infinite magnets, Proc. of 3rd Joint INTERMAG-Magnetism and Magnetic Materials (MMM) Conference at Montreal, Quebec, Canada; J. Appl. Phys.53, 7914 (1982)Google Scholar
- 9.Leibler, S., Peliti, L.: J. Phys. C30, L403 (1982)Google Scholar
- 10.Rudnick, J., Jasnow, D.: Phys. Rev. Lett.48, 1059 (1982)Google Scholar
- 11.Brézin, E., Leibler, S.: CEN-Saclay preprint DPh-T/82-52Google Scholar
- 12.Bray, A.J., Moore, M.A.: J. Phys. A10, 1927 (1977)Google Scholar
- 13.Cordery, R., Griffin, A.: Ann. Phys.134, 411 (1981)Google Scholar
- 14.Reeve, J.S.: Phys. Lett.81 A, 237 (1981)Google Scholar
- 15.Reeve, J.S., Guttmann, A.J.: J. Phys. A14, 3357 (1981)Google Scholar
- 16.Au-Yang, H.: J. Math. Phys.14, 937Google Scholar
- 17.Mermin, N.D., Wagner, H.: Phys. Rev. Lett.17, 1133 (1966)Google Scholar
- 18.Mills, D.L., Maradudin, A.A.: J. Phys. Chem. Solids28, 1855Google Scholar
- 19.Mills, D.L.: Comm. Solid State Phys4, 28 (1971);5, 95 (1971)Google Scholar
- 20.Kosterlitz, J.M., Thouless, D.J.: J. Phys. C6, 1181 (1973)Google Scholar
- 21.Diehl, H.W., Eisenriegler, E.: Phys. Rev. Lett.48, 1767 (1982)Google Scholar
- 22.Lubensky, T.C., Rubin, M.H.: Phys. Rev. B12, 3885 (1975)Google Scholar
- 23.Kumar, P., Maki, K.: Phys. Rev. B13, 2011 (1976)Google Scholar
- 24.Lubensky, T.C., Rubin, M.H.: Phys. Rev. B11, 4533 (1975)Google Scholar
- 25.Bogoliubov, N.N., Shirkov, D.V.: Introduction to the Theory of Quantized Fields. New York: Interscience 1959Google Scholar
- 26.Gelfand, I.M., Shilov, G.E.: Generalized functions, Vol. 1. New York: Academic Press 1964Google Scholar
- 27.Gradsteyn, I.S., Rhyzik, I.M.: Table of integrals, series, and products. New York: Academic Press 1980Google Scholar