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Critical behavior of short range Potts glasses

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Zeitschrift für Physik B Condensed Matter

Abstract

We study by means of Monte Carlo simulations and the numerical transfer matrix technique the critical behavior of the short rangep=3 state Potts glass model in dimensionsd=2,3,4 with both Gaussian and bimodal (±J) nearest neighbor interactions on hypercubic lattices employing finite size scaling ideas. Ind=2 in addition the degeneracy of the glass ground state is computed as a function of the number of Potts states forp=3, 4, 5 and compared to that of the antiferromagnetic ground state. Our data indicate a transition into a glass phase atT=0 ind=2 with an algebraic singularity, aT=0 transition ind=3 with an essential singularity of the form χ∼exp(const.T −2), and an algebraic singularity atT≈0.25 ind=4. We conclude that the lower critical dimension of the present model isd c =3 or very close to it. Some of the critical exponents are estimated and their respective values discussed.

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References

  1. Toulouse, G.: Commun. Phys.2, 115 (1977)

    Google Scholar 

  2. Binder, K., Young, A.P.: Rev. Mod. Phys.58, 801 (1986)

    Google Scholar 

  3. Young, A.P., Reger, J.D., Binder, K.: In: The Monte Carlo method in condensed matter physics, p. 355, Binder, K. (ed.). Berlin, Heidelberg, New York: Springer 1992

    Google Scholar 

  4. Sullivan, N.S., Devoret, M., Esteve, D.: Phys. Rev. B30, 4935 (1984)

    Google Scholar 

  5. Potts, R.B.: Proc. Camb. Philos. Soc.48, 106 (1952)

    Google Scholar 

  6. Wu, F.Y.: Rev. Mod. Phys.54, 235 (1982)

    Google Scholar 

  7. Lieb, E.: Phys. Rev.162, 162 (1967)

    Google Scholar 

  8. Goldbart, P.M., Sherrington, D.: J. Phys. C18, 1923 (1985)

    Google Scholar 

  9. Binder, K., Reger, J.D.: Theory of orientational glasses: models, concepts, simulations. Adv. Phys.41, 547 (1992)

    Google Scholar 

  10. Carmesin, H.-O.: J. Phys. A22, 297 (1989)

    Google Scholar 

  11. Knorr, K.: Phys. Scri. T19, 531 (1989); Loidl, A.: Annu. Rev. Phys. Chem.40, 29 (1989)

    Google Scholar 

  12. Edwards, S.F., Anderson, P.W.: J. Phys. F5, 965 (1975)

    Google Scholar 

  13. Parisi, G.: J. Phys. A13, 1101, 1887, L115 (1980); Philos. Mag.41, 677 (1980); Phys. Rep.67, 97 (1980); Phys. Rev. Lett.50, 1946 (1983)

    Google Scholar 

  14. Elderfeld, D.J., Sherrington, D.: J. Phys. C16, L479, L971, L1169 (1983); Elderfield, D.J.: J. Phys.A17, L517 (1984)

    Google Scholar 

  15. Gross, D.J., Kanter, I., Sompolinsky, H.: Phys. Rev. Lett.55, 304 (1985)

    Google Scholar 

  16. Cwilich, G.: J. Phys. A23, 5029 (1990); Cwilich, G., Kirkpatrick, T.R.: J. Phys. A22, 4971 (1989)

    Google Scholar 

  17. Derrida, B.: Phys. Rev. Lett.45, 789 (1980); Phys. Rev. B24, 2613 (1981); Gross, D.J., Mezard, M.: Nucl. Phys. B240, 431 (1984)

    Google Scholar 

  18. Kirkpatrick, T.R., Thirumalai, D.: Phys. Rev. B36, 5388 (1987)

    Google Scholar 

  19. Kirkpatrick, T.R., Thirumalai: Phys. Rev. B37, 5342 (1988)

    Google Scholar 

  20. Leutheusser, A.: Phys. Rev. A29, 2765 (1984); Götze, W.: Phys. Rev. B60, 195 (1985); Bengtzelius, U.: Phys. Rev. A33, 3433 (1986)

    Google Scholar 

  21. Kirkpatrick, T.R., Wolynes, P.G.: Phys. Rev. A35, 3072 (1987);

    Google Scholar 

  22. Kirkpatrick, T.R., Wolynes, P.G.: Phys. Rev. B36, 8552 (1987)

    Google Scholar 

  23. Scheucher, M.: Dissertation (Thesis), Universität Mainz, 1990

  24. Scheucher, M., Reger, J.D., Binder, K., Young, A.P.: Phys. Rev. B42, 6881 (1990)

    Google Scholar 

  25. Scheucher, M., Reger, J.D., Binder, K., Young, A.P.: In: Computer simulations in condensed matter physics III. Landau, D.P., Mon, K.K., Schüttler, H.B. (eds.). Berlin, Heidelberg, New York: Springer 1991

    Google Scholar 

  26. Scheucher, M., Reger, J.D.: Phys. Rev. B45, 2499 (1992)

    Google Scholar 

  27. Scheucher, M., Reger, J.D., Binder, K., Young, A.P.: Europhys. Lett.14, 119 (1991)

    Google Scholar 

  28. Scheucher, M., Reger, J.D., Young, A.P.: Europhys. Lett.20, 343 (1992)

    Google Scholar 

  29. Carmesin, H.-O., Binder, K.: J. Phys. A21, 4053 (1988)

    Google Scholar 

  30. Privman, V.: In: Finite size scaling and numerical simulations of statistical systems, p. 1. Privman, V. (ed.). Singapore: World Scientific 1990

    Google Scholar 

  31. Young, A.P.: In: Finite size scaling and numerical simulations of statistical systems, p. 465. Privman, V. (ed.). Singapore: World Scientific 1990

    Google Scholar 

  32. Binder, K.: Z. Phys. B43, 119 (1981); Ferroelectrics43, 73 (1987)

    Google Scholar 

  33. McMillan, W.L.: J. Phys. C17, 3179 (1984)

    Google Scholar 

  34. Reger, J.D., Young, A.P.: Phys. Rev. B37, 5493 (1988)

    Google Scholar 

  35. Bhatt, R.N., Young, A.P.: Phys. Rev. Lett.54, 924 (1985); Phys. Rev. B37, 5606 (1988); and in: Proceedings of the Heidelberg colloquium on glassy dynamics, p. 215. van Hemmen, L., Morgenstern, I. (eds.). Berlin, Heidelberg, New York: Springer 1987

    Google Scholar 

  36. Reger, J.D., Bhatt, R.N., Young, A.P.: Phys. Rev. Lett.64, 1859 (1990); Bhatt, R.N., Reger, J.D., Young, A.P.: J. Appl. Phys.69, 5219 (1991)

    Google Scholar 

  37. Banavar, J.R., Cieplak, M.: Phys. Rev. B39, 9633 (1988)

    Google Scholar 

  38. Singh, R.R.P.: Phys. Rev. B43, 6299 (1991)

    Google Scholar 

  39. Bray, A.J., Moore, M.A.: In: Proceedings of the Heidelberg colloquium on glassy dynamics p. 121. van Hemmen, L., Morgenstern, I. (eds.). Berlin, Heidelberg, New York: Springer 1987

    Google Scholar 

  40. Morgenstern, I., Binder, K.: Phys. Rev. B22, 288 (1980); Morgenstern, I.: In: Springer Lecture Notes in Physics, Vol. 19. van Hemmen, L., Morgenstern, I. (eds.). Berlin, Heidelberg, New York: Springer 1983

    Google Scholar 

  41. Wang, J.-S., Swendsen, R.H., Kotecky: Phys. Rev. B42, 2465 (1990)

    Google Scholar 

  42. Scheucher, M., Reger, J.D.: unpublished (1991)

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Author notes

  1. M. Scheucher

    Present address: Systemtechnik Berner & Mattner, Otto-Hahn-Strasse 34, W-8012, München-Ottobrunn, Germany

Authors and Affiliations

  1. Institut für Physik, Universität Mainz, Staudingerweg 7, W-6500, Mainz, Germany

    M. Scheucher & J. D. Reger

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  1. M. Scheucher
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  2. J. D. Reger
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Scheucher, M., Reger, J.D. Critical behavior of short range Potts glasses. Z. Physik B - Condensed Matter 91, 383–396 (1993). https://doi.org/10.1007/BF01344068

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