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Correlation functions in one-dimensional spin lattices with Ising and Heisenberg bonds

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Abstract

A general technique of exact calculation of any correlation functions for the special class of one-dimensional spin models containing small clusters of quantum spins assembled to a chain by alternating with the single Ising spins is proposed. The technique is a natural generalization of that in the models solved by a classical transfer matrix. The general expressions for corresponding matrix operators which are the key components of the technique are obtained. As it is clear from the general principles, the decay of the correlation functions of various types is explicitly shown to be governed by a single correlation length. The technique is illustrated by two examples: symmetric diamond chain and asymmetric sawtooth chain.

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References

  1. J. Strečka, M. Jaščur, J. Phys.: Condens. Matter 15, 4519 (2003)

    ADS  Google Scholar 

  2. J. Strečka, M. Hagiwara, M. Jaščur, K. Minami, Czech. J. Phys. 54, D583 (2004)

    Article  ADS  Google Scholar 

  3. J. Strečka, M. Jaščur, M. Hagiwara, Y. Narumi, K. Kindo, K. Minami, Phys. Rev. B 72, 024459 (2005)

    Article  ADS  Google Scholar 

  4. L. Čanová, J. Strečka, M. Jaščur, J. Phys.: Condens. Matter 18, 4967 (2006)

    Google Scholar 

  5. J.S. Valverde, O. Rojas, S.M. de Souza, J. Phys.: Condens. Matter 20, 345208 (2008)

    Google Scholar 

  6. M.S.S. Pereira, F.A.B.F. de Moura, M.L. Lyra, Phys. Rev. B 77, 024402 (2008)

    Article  ADS  Google Scholar 

  7. M.S.S. Pereira, F.A.B.F. de Moura, M.L. Lyra, Phys. Rev. B 79, 054427 (2009)

    Article  ADS  Google Scholar 

  8. J. Strečka, L. Čanová, T. Lučivjanský, M. Jaščur, J. Phys.: Conf. Ser. 145, 012058 (2009)

    ADS  Google Scholar 

  9. D. Antonosyan, S. Bellucci, V. Ohanyan, Phys. Rev. B 79, 014432 (2009)

    Article  ADS  Google Scholar 

  10. V. Ohanyan, Condens. Matter Phys. 12, 343 (2009)

    Article  Google Scholar 

  11. V. Ohanyan, Phys. Atomic Nucl. 73, 494 (2010)

    Article  ADS  Google Scholar 

  12. J. Strečka, L. Galisova, O. Derzhko, Acta Phys. Pol. A 118, 742 (2010)

    Google Scholar 

  13. S. Bellucci, V. Ohanyan, Eur. Phys. J. B 75, 531 (2010)

    Article  MATH  ADS  Google Scholar 

  14. O. Rojas, S.M. de Souza, V. Ohanyan, M. Khurshudyan, Phys. Rev. B 83, 094430 (2011)

    Article  ADS  Google Scholar 

  15. O. Rojas, S.M. de Souza, Phys. Lett. A 375, 1295 (2011)

    Article  MATH  ADS  Google Scholar 

  16. B. Lisnii, Low Temp. Phys. 37, 296 (2011)

    Article  ADS  Google Scholar 

  17. B. Lisnii, Ukr. J. Phys. 56, 1237 (2011)

    Google Scholar 

  18. J. Strečka, M. Dančo, Physica B 406, 2967 (2011)

    Article  ADS  Google Scholar 

  19. V. Ohanyan, A. Honecker, Phys. Rev. B 86, 054412 (2012)

    Article  ADS  Google Scholar 

  20. L. Chakhmakhchyan, N. Ananikian, L. Ananikyan, Č. Burdık, J. Phys.: Conf. Ser. 343, 012022 (2012)

    ADS  Google Scholar 

  21. O. Rojas, S.M. de Souza, N.S. Ananikian, Phys. Rev. E 85, 061123 (2012)

    Article  ADS  Google Scholar 

  22. N. Ananikian, L. Ananikyan, L. Chakhmakhchyan, O. Rojas, J. Phys.: Condens. Matter 24, 256001 (2012)

    ADS  Google Scholar 

  23. T. Verkholyak, J. Strečka, J. Phys. A 45, 305001 (2012)

    Article  MathSciNet  Google Scholar 

  24. J. Strečka, M. Hagiwara, Y. Han, T. Kida, Z. Honda, M. Ikeda, Condens. Matter Phys. 15, 43002 (2012)

    Article  Google Scholar 

  25. L. Galisova, Phys. Stat. Sol. (b) 250, 187 (2013)

    Article  ADS  Google Scholar 

  26. O. Rojas, M. Rojas, N.S. Ananikian, S.M. de Souza, Phys. Rev. A 86, 042330 (2012)

    Article  ADS  Google Scholar 

  27. R. Baxter, Exactly Solved Models in Statistical Mechanics (Academic Press, New York, 1982)

  28. V. Ohanyan, N. Ananikian, Phys. Lett. A 307, 76 (2003)

    Article  MATH  ADS  Google Scholar 

  29. E. Aydiner, C. Akyüz, Chin. Phys. Lett. 22, 2382 (2005)

    Article  Google Scholar 

  30. E. Aydiner, C. Akyüz, M. Gönülol, H. Polat, Phys. Stat. Sol. (b) 243, 2901 (2006)

    Article  ADS  Google Scholar 

  31. D. Gatteschi, R. Sessoli, J. Villain, Molecular Nanomagnets (Oxford Univ. Press, New York, 2007)

  32. D. Visinescu, A.M. Madalan, M. Andruh, C. Duhayon, J.-P. Sutter, L. Ungur, W. Van den Heuvel, L.F. Chibotaru, Chem. Eur. J. 15, 11808 (2009)

    Article  Google Scholar 

  33. J. Rinck, G. Novitchi, W. Van den Heuvel, L. Ungur, Y. Lan, W. Wernsdorfer, C.E. Anson, L.F. Chibotaru, A.K. Powell, Angew. Chem. Int. Ed. 49, 7583 (2010)

    Article  Google Scholar 

  34. W. Van den Heuvel, L.F. Chibotaru, Phys. Rev. B 82, 174436 (2010)

    Article  ADS  Google Scholar 

  35. V. Ravi Chandra, S. Ramasesha, D. Sen, Phys. Rev. B 70, 144404 (2004)

    Article  ADS  Google Scholar 

  36. T.S. Venkatakrishnan, S. Sahoo, N. Bréfuel, C. Duhayon, C. Paulsen, A.-L. Barra, S. Ramasesha, J.-P. Sutter, J. Am. Chem. Soc. 132, 6047 (2010)

    Article  Google Scholar 

  37. S. Sahoo, J.-P. Sutter, S. Ramasesha, J. Stat. Phys. 147, 181 (2012)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  38. M.E. Fisher, Phys. Rev. 113, 969 (1959)

    Article  ADS  Google Scholar 

  39. O. Rojas, J.S. Valverde, S.M. de Souza, Physica A 388, 1419 (2009)

    Article  MathSciNet  ADS  Google Scholar 

  40. J. Strečka, Phys. Lett. A 374, 3718 (2010)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  41. M. Knežević, S. Milošević, J. Phys. Gen. 13, 2479 (1980)

    Article  Google Scholar 

  42. R.J.V. dos Santos, M.L. Lyra, Physica A 182, 133 (1992)

    Article  ADS  Google Scholar 

  43. J. Strečka, L. Čanová, K. Minami, Phys. Rev. B 79, 051103 (2009)

    Article  ADS  Google Scholar 

  44. J. Strečka, O. Rojas, S.M. de Souza, Eur. Phys. J. B 85, 54 (2010)

    Article  ADS  Google Scholar 

  45. J. Čiśarova, J. Strečka, Phys. Rev. B 87, 024421 (2013)

    Article  Google Scholar 

  46. J. Čiśarova, F. Michaud, F. Mila, J. Strečka, Phys. Rev. B 87, 054419 (2013)

    Article  ADS  Google Scholar 

Download references

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Authors and Affiliations

  1. INFN-Laboratori Nazionali di Frascati, Via E. Fermi 40, 00044, Frascati, Italy

    Stefano Bellucci

  2. Department of Theoretical Physics, Yerevan State University, Alex Manoogian 1, 0025, Yerevan, Armenia

    Vadim Ohanyan

  3. ICTP, Strada Costiera 11, 34151, Trieste, Italy

    Vadim Ohanyan

Authors
  1. Stefano Bellucci
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  2. Vadim Ohanyan
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Correspondence to Vadim Ohanyan.

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Bellucci, S., Ohanyan, V. Correlation functions in one-dimensional spin lattices with Ising and Heisenberg bonds. Eur. Phys. J. B 86, 446 (2013). https://doi.org/10.1140/epjb/e2013-40336-4

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  • DOI: https://doi.org/10.1140/epjb/e2013-40336-4

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