Zeitschrift für Physik B Condensed Matter

, Volume 75, Issue 1, pp 109–118 | Cite as

Diagrammatic perturbation approach to finite-size and surface critical behavior for Dirichlet boundary conditions



A recent field-theoretic treatment of finite-size effects in the presence of Dirichlet boundary conditions is developed further. A simplified perturbation approach is introduced that makes higher orders amenable to diagrammatic evaluation. As an illustration the surface energy and surface specific heat are calculated up to two-loop order. Further suggestions of future research are discussed.


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  1. 1.
    Brézin, E., Zinn-Justin, J.: Nucl. Phys.B 257 [FS14], 867 (1985)Google Scholar
  2. 2.
    Rudnick, J., Guo, H., Jasnow, D.: J. Stat. Phys.41, 353 (1985)Google Scholar
  3. 3.
    Huhn, W., Dohm, V.: Phys. Rev. Lett.61, 1368 (1988)Google Scholar
  4. 4.
    Diehl, H.W.: In: Phase transitions and critical phenomena. Domb, C., Lebowitz, J.L. (eds.), Vol. 10. New York: Academic Press 1983Google Scholar
  5. 5.
    Dohm, V.: J. Low Temp. Phys.69, 51 (1987)Google Scholar
  6. 6.
    Chen, T.P., Gasparini, F.M.: Phys. Rev. Lett.40, 331 (1978)Google Scholar
  7. 7.
    Ahlers, G.: Private communicationGoogle Scholar
  8. 8.
    Donnelly, R.J.: Private communicationGoogle Scholar
  9. 9.
    Gasparini, F.M.: Private communicationGoogle Scholar
  10. 10.
    In an earlier approach [Eisenriegler, E.: Z. Phys. B—Condensed Matter61, 299 (1985)] only the region ξ≪L could be treated systematicallyGoogle Scholar
  11. 11.
    Goldschmidt, Y.Y., Jasnow, D.: Phys. Rev.B 29, 3990 (1984). I thank D. Frank for bringing this work to my attentionGoogle Scholar
  12. 12.
    Guo, H., Jasnow, D.: Phys. Rev.B 35 1846 (1987)Google Scholar
  13. 13.
    Huhn, W.: Dissertation, TH Aachen (1988)Google Scholar
  14. 14.
    Huhn, W., Dohm, V.: (to be published)Google Scholar
  15. 15.
    Rudnick, J., Gaspari, G., Privman, V.: Phys. Rev.B 32, 7594 (1985)Google Scholar
  16. 16.
    Wacker, A.: Diplomarbeit, TH Aachen (1989)Google Scholar
  17. 17.
    Dohm, V.: Z. Phys. B—Condensed Matter60, 61 (1985)Google Scholar
  18. 18.
    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
  19. 19.
    Amit, D.J.: Field theory, the renormalization group, and critical phenomena. New York: McGraw-Hill 1978Google Scholar
  20. 20.
    Dietrich, S., Diehl, H.W.: Z. Phys. B—Condensed Matter43, 315 (1981)Google Scholar
  21. 21.
    Frank, D., Dohm, V.: (to be published)Google Scholar
  22. 22.
    Schloms, R., Dohm, V.: Europhys. Lett.3, 413 (1987)Google Scholar
  23. 23.
    Brézin, E.: J. Phys. (Paris)43 15 (1982)Google Scholar
  24. 24.
    Privman, V., Fisher, M.E.: J. Phys. A.16, L295 (1983)Google Scholar
  25. 25.
    Wegner, F.: Phys. Rev. B5, 4529 (1972)Google Scholar
  26. 26.
    Ginzburg, V.L., Pitaevskii, L.P.: Sov. Phys. JETP7, 858 (1958)Google Scholar
  27. 27.
    Frank, D., Grabinski, M., Dohm, V., Liu, M.: Phys. Rev. Lett.60, 2336 (1988)Google Scholar
  28. 28.
    Halperin, B.I., Hohenberg, P.C., Siggia, E.D.: Phys. Rev. B13, 1299 (1976); Dohm, V.: Z. Phys. B—Condensed Matter61, 193 (1985)Google Scholar
  29. 29.
    Duncan, R.V., Ahlers, G., Steinberg, V.: Phys. Rev. Lett.58, 377 (1987)Google Scholar
  30. 30.
    Ahlers, G., Duncan, R.V.: Phys. Rev. Lett.61, 846 (1988)Google Scholar
  31. 31.
    Barber, M.N., Pearson, R.B., Toussaint, D., Richardson, J.L.: Phys. Rev. B32, 1720 (1985); Binder, K.: Ferroelectrics73, 43 (1987)Google Scholar
  32. 32.
    Liu, A.J., Fisher, M.E.: The three-dimensional, Ising model revisited numerically. PreprintGoogle Scholar
  33. 33.
    Krause, H.J.: Diplomarbeit, TH Aachen (1989)Google Scholar

Copyright information

© Springer-Verlag 1989

Authors and Affiliations

  • V. Dohm
    • 1
  1. 1.Institute for Physical Science and TechnologyUniversity of MarylandCollege ParkUSA

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