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Spin-glass-type state in complex nonmagnetic systems

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Abstract

We briefly review our works concerned with generalized models of spin glass, which describe a wide class of glasses (multipole systems, real cluster glasses, and others). We consider several new models and discuss how the scenario of glass transition depends on different factors. We propose a classification of the behaviors of complex spin glasses depending on the system symmetry properties.

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References

  1. N. N. Bogoliubov, “Quasi-averages in problems of statistical mechanics [in Russian],” Preprint No. D-781, Joint Inst. Nucl. Res., Dubna (1963); “Quasi-averages in problems of statistical mechanics,” in: Selected works [in Russian], Vol. 3, Naukova Dumka, Kiev (1971), pp. 174–243.

    Google Scholar 

  2. V. A. Moskalenko, M. I. Vladimir, and S. P. Kozhukar’, The Consistent Field Method in the Theory of Glassy States of Spin and Quadrupole Systems [in Russian], Shtiintsa, Kishinev (1990).

    Google Scholar 

  3. M. Mézard, G. Parisi, and M. Virasoro, Spin Glass Theory and Beyond (Lect. Notes Phys., Vol. 9), World Scientific, Singapore (1987).

    MATH  Google Scholar 

  4. S. F. Edwards and P. W. Anderson, J. Phys. F, 5, 965–974 (1975).

    Article  ADS  Google Scholar 

  5. D. Sherrington and S. Kirkpatrick, Phys. Rev. Lett., 35, 1972–1976 (1975); S. Kirkpatrick and D. Sherrington, Phys. Rev. B, 17, 4384–4403 (1978).

    Article  Google Scholar 

  6. J. R. L. Almeida and D. J. Thouless, J. Phys. A, 11, 983–990 (1978).

    Article  ADS  Google Scholar 

  7. G. Parisi, J. Phys. A, 13, L115–L121 (1980).

    Article  ADS  Google Scholar 

  8. G. Parisi, J. Phys. A, 13, 1887–1895 (1980).

    Article  ADS  MathSciNet  Google Scholar 

  9. T. R. Kirkpatrick and D. Thirumalai, Phys. Rev. B, 36, 5388–5397 (1987); 37, 5342–5350 (1988); T. R. Kirkpatrick and P. G. Wolynes, Phys. Rev. B, 36, 8552–8564 (1987).

    Article  ADS  Google Scholar 

  10. P. Goldbart and D. Elderfield, J. Phys. C, 18, L229–L233 (1985).

    Article  ADS  Google Scholar 

  11. M. Campellone, B. Coluzzi, and G. Parisi, Phys. Rev. B, 58, 12081–12089 (1998).

    Article  ADS  Google Scholar 

  12. N. V. Gribova and E. E. Tareyeva, Theor. Math. Phys., 131, 852–861 (2002).

    Article  MATH  Google Scholar 

  13. N. V. Gribova, V. N. Ryzhov, T. I. Schelkacheva, and E. E. Tareyeva, Phys. Lett. A, 315, 467–473 (2003).

    Article  MATH  ADS  Google Scholar 

  14. E. A. Lutchinskaia, V. N. Ryzhov, and E. E. Tareyeva, J. Phys. C, 17, L665–L667 (1984); Theor. Math. Phys., 67, 623–627 (1986); E. A. Lutchinskaia and E. E. Tareyeva, Phys. Rev. B, 52, 366–373 (1995).

    Article  ADS  Google Scholar 

  15. N. S. Sullivan, C. M. Edwards, and J. R. Brookeman, Mol. Cryst. Liq. Cryst., 139, 365–375 (1986).

    Article  Google Scholar 

  16. K. Walasek, Phys. Rev. B, 46, 14480–14485 (1992); K. Walasek and K. Lukerska-Walasek, Phys. Rev. B, 49, 9460–9468, 9973–9976 (1994).

    Article  ADS  Google Scholar 

  17. T. K. Kopeć, Phys. Rev. B, 48, 15658–15665, 16792–16794 (1993).

    Article  ADS  Google Scholar 

  18. T. I. Schelkacheva, E. E. Tareyeva, and N. M. Chtchelkatchev, Phys. Rev. E, 79, 021105 (2009).

    Google Scholar 

  19. E. Gardner, Nucl. Phys. B, 257, 747–765 (1985).

    Article  ADS  Google Scholar 

  20. A. F. Goncharov, J. H. Eggert, I. I. Mazin, R. J. Hemley, and H.-K. Mao, Phys. Rev. B, 54, R15590–R15593 (1996).

    Article  ADS  Google Scholar 

  21. E. E. Tareyeva, T. I. Schelkacheva, and N. M. Chtchelkatchev, Theor. Math. Phys., 155, 812–823 (2008).

    Article  MATH  Google Scholar 

  22. T. I. Schelkacheva, E. E. Tareyeva, and N. M. Chtchelkatchev, Phys. Rev. B, 76, 195408 (2007).

    Article  ADS  Google Scholar 

  23. B. Sundqvist, Adv. Phys., 48, 1–134 (1999).

    Article  ADS  Google Scholar 

  24. R. Moret, Acta Cryst. A, 61, 62–76 (2005).

    Article  Google Scholar 

  25. R. Heid, Phys. Rev. B, 47, 15912–15922 (1993).

    Article  ADS  Google Scholar 

  26. V. N. Ryzhov, E. E. Tareyeva, T. I. Schelkacheva, and N. M. Chtchelkatchev, Theor. Math. Phys., 141, 1443–1451 (2004).

    Article  Google Scholar 

  27. N. M. Chtchelkatchev, V. N. Ryzhov, T. I. Schelkacheva, and E. E. Tareyeva, Phys. Lett. A, 329, 244–249 (2004).

    Article  MATH  ADS  Google Scholar 

  28. L. F. Cugliandolo, “Course 7: Dynamics of glassy systems,” in: Slow Relaxations and Nonequilibrium Dynamics in Condensed Matter (Les Houches, Vol. 77, J.-L. Barrat, M. Feigelman, J. Kurchan, and J. Dalibard, eds.), Springer, Berlin (2004), pp. 161–171; arXiv:cond-mat/0210312v2 (2002).

    Google Scholar 

  29. V. N. Ryzhov, J. Phys., 2, 5855–5865 (1990); V. N. Ryzhov, Theor. Math. Phys., 80, 745–752 (1989).

    Google Scholar 

  30. V. N. Ryzhov and E. E. Tareyeva, J. Phys. C, 21, 819–824 (1988); Phys. Rev. B, 51, 8789–8794 (1995); Phys. A, 314, 396–404 (2002); Theor. Math. Phys., 73, 1344–1352 (1987); 92, 922–930 (1992).

    Article  ADS  Google Scholar 

  31. E. A. Luchinskaya and E. E. Tareeva, Theor. Math. Phys., 90, 185–188 (1992).

    Article  MathSciNet  Google Scholar 

  32. T. I. Schelkacheva, E. E. Tareyeva, and N. M. Chtchelkatchev, Phys. Lett. A, 358, 222–226 (2006).

    Article  MATH  ADS  Google Scholar 

  33. N. V. Gribova, V. N. Ryzhov, and E. E. Tareyeva, Phys. Rev. E, 68, 067103 (2003).

    Google Scholar 

  34. A. Crisanti and L. Leuzzi, Phys. Rev. Lett., 93, 217203 (2004); Phys. Rev. B, 73, 014412 (2006).

    Google Scholar 

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Correspondence to E. E. Tareyeva.

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Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 160, No. 2, pp. 385–400, August, 2009.

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Tareyeva, E.E., Schelkacheva, T.I. & Chtchelkatchev, N.M. Spin-glass-type state in complex nonmagnetic systems. Theor Math Phys 160, 1190–1202 (2009). https://doi.org/10.1007/s11232-009-0110-7

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