Zeitschrift für Physik B Condensed Matter

, Volume 90, Issue 2, pp 229–239 | Cite as

Properties of interfaces in the two and three dimensional Ising model

  • B. A. Berg
  • U. Hansmann
  • T. Neuhaus
Original Contributions


To investigate order-order interfaces, we perform multimagnetical Monte Carlo simulations of the 2D and 3D Ising model. Following Binder we extract the interfacial free energy from the infinite volume limit of the magnetic probability density. Stringent tests of the numerical methods are performed by reproducing with high precision exact 2D results. In the physically more interesting 3D case we estimate the amplitudeF 0 s of the critical interfacial tensionF3=F 0 s tμ to beF 0 s =1.52±0.05. This result is in good agreement with a previous MC calculation by Mon, as well as with experimental results for related amplitude ratios. In addition, we study in some details the shape of the magnetic probability density for temperatures below the Curie point.


Neural Network Free Energy Monte Carlo Simulation Ising Model Amplitude Ratio 
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  1. 1.
    Onsager, L.: Phys. Rev.65, 117 (1944)Google Scholar
  2. 2.
    Rottmann, C., Wortis, M.: Phys. Rev. B24, 6274 (1981)Google Scholar
  3. 3.
    Shlosman, S.B.: Commun. Math. Phys.125, 81 (1989)Google Scholar
  4. 4.
    Binder, K.: Z. Phys. B — Condensed Matter43, 119 (1981)Google Scholar
  5. 5.
    Binder, K.: Phys. Rev. A25, 1699 (1982)Google Scholar
  6. 6.
    Mon, K.K.: Phys. Rev. Lett.60, 2749 (1988)Google Scholar
  7. 7.
    Meyer-Ortmanns, H., Trappenberg, T.: J. Stat. Phys.58, 185 (1990)Google Scholar
  8. 8.
    Fis, S., Widom, B.: J. Chem. Phys.50, 3219 (1969)Google Scholar
  9. 9.
    Stauffer, D., Ferer, M., Wortis, M.: Phys. Rev. Lett.29, 345 (1972)Google Scholar
  10. 10.
    Moldover, M.R.: Phys. Rev. A31, 1022 (1984); Chaar, H., Moldover, M.R., Schmidt, J.W.: J. Chem. Phys.85, 418 (1986)Google Scholar
  11. 11.
    Gielen, H.L., Verbeke, O.B., Thoen, J.: J. Chem. Phys.84, 6154 (1984)Google Scholar
  12. 12.
    Fisher, M.E., Wen, H.: Phys. Rev. Lett.68, 3654 (1992)Google Scholar
  13. 13.
    Widom, B.: J. Chem. Phys.43, 3892 (1965)Google Scholar
  14. 14.
    Zinn-Justin, J.: J. Phys. (Paris)42, 783 (1981)Google Scholar
  15. 15.
    Alves, N.A., Berg, B.A., Villanova, R.: Phys. Rev. B41, 383 (1989)Google Scholar
  16. 16.
    Liu, A.J., Fisher, M.E.: Physica A156, 35 (1989)Google Scholar
  17. 17.
    Jansen, K., Montvay, I., Münster, G., Trappenberg, T., Wolff, U.: Nucl. Phys. B322, 698 (1989)Google Scholar
  18. 18.
    Berg, B., Neuhaus, T.: Phys. Lett. B267, 249 (1991); Phys. Rev. Lett.68, 9 (1989)Google Scholar
  19. 19.
    Berg, B., Hansmann, U., Neuhaus, T.: Preprint, SCRI-91-125. Phys. Rev. B (submitted for publication)Google Scholar
  20. 20.
    Alves, N.A., Berg, B., Sanielevici, S.: Nucl. Phys. B376, 218 (1992)Google Scholar
  21. 21.
    Ferrenberg, A.M., Swendsen, R.H.: Phys. Rev. Lett.61, 2635 (1988);63, 1658 (E) (1989), and references given in the erratum; Falcioni, M., Marinari, E., Paciello, M.L., Parisi, G., Taglienti, B.: Phys. Lett. B108, 331 (1982)Google Scholar
  22. 22.
    Yang, C.N.: Phys. Rev.85, 808 (1952)Google Scholar
  23. 23.
    Borgs, C., Kotecký, R.: J. Stat. Phys.61, 79 (1990); and Borgs, C.: Private communicationGoogle Scholar
  24. 24.
    Mon, K.K., Landau, D.P., Stauffer, D.: Phys. Rev. B42, 545 (1990)Google Scholar
  25. 25.
    Wulf, G.: Z. Kristallogr. Mineral.34, 449 (1901)Google Scholar
  26. 26.
    Hansmann, U., Berg, B., Neuhaus, T.: Proceedings of the workshop Dynamics of First Order Phase Transitions, Jülich, June 1–3, 1992. Int. J. Mod. Phys. C (to be published)Google Scholar
  27. 27.
    Klessinger, S., Münster, G.: Preprint, Münster University, Germany, MS-TPI-92-13Google Scholar
  28. 28.
    Gausterer, H., Potvin, J., Rebbi, C., Sanielevici, S.: Preprint, Boston University, BU-HEP-92-16Google Scholar
  29. 29.
    Wiese, U.J.: Preprint BUTP-92/37Google Scholar

Copyright information

© Springer-Verlag 1993

Authors and Affiliations

  • B. A. Berg
    • 1
    • 2
  • U. Hansmann
    • 1
    • 2
  • T. Neuhaus
    • 3
  1. 1.Department of PhysicsThe Florida State UniversityTallahasseeUSA
  2. 2.Supercomputer Computations Research Institute TallahasseeThe Florida State UniversityTallahasseeUSA
  3. 3.Fakultät für PhysikUniversität BielefeldBielefeldFederal Republic of Germany

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