Analysis of a long-range random field quantum antiferromagnetic Ising model

Solid and Condensed State Physics

Abstract.

We introduce a solvable quantum antiferromagnetic model. The model, with Ising spins in a transverse field, has infinite range antiferromagnetic interactions and random fields on each site following an arbitrary distribution. As is well-known, frustration in the random field Ising model gives rise to a many valley structure in the spin-configuration space. In addition, the antiferromagnetism also induces a regular frustration even for the ground state. In this paper, we investigate analytically the critical phenomena in the model, having both randomness and frustration and we report some analytical results for it.

PACS.

75.50.L Spin glasses and other random magnets 05.30.-d Quantum statistical mechanics 02.50.-r Probability theory, stochastic processes, and statistics 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. See e.g., E. Fradkin, Field Theories of Condensed Matter Systems (Addison-Wesley, Redwood, 1991); I. Bose, in Frontiers in Condensed Matter Physics: 75th year special publication of Ind. J. Phys., edited by J.K. Bhattacharjee, B.K. Chakrabarti (Allied Publ., New Delhi, 2005) Google Scholar
  2. B.K. Chakrabarti, A. Dutta, P. Sen, Quantum Ising Phases and Transitions in Transverse Ising Models (Springer, Heidelberg, 1996) Google Scholar
  3. M. Suzuki, Prog. Theor. Phys. 56, 2454 (1976); see also B.K. Chakrabarti, A. Das, pp. 3-36 and N. Hatano, M. Suzuki, pp. 37-68 in Quantum Annealing and Related Optimization Methods, edited by A. Das, B.K. Chakrabarti, LNP 679 (Springer, Heidelberg, 2005) Google Scholar
  4. See, e.g., P.M. Chaikin, T.C. Lubensky, Principles of Condensed Matter Physics (Cambridge University Press, Cambridge, 1997) Google Scholar
  5. B.K. Chakrabarti, J. Inoue, e-print arXiv:cond-mat/0508218 (2005); Proc. CMDAYS-05, Ind. J. Phys. 80 (No.6) (2005) (to be published) Google Scholar
  6. See e.g., C. Kittel, Introduction to Solid State Physics (John Wiley & Sons Inc., N.Y., 1966) Google Scholar
  7. D. Sherrington, S. Kirkpatrick, Phys. Rev. Lett. 35, 1792 (1975) CrossRefADSGoogle Scholar
  8. T. Schneider, E. Pytte, Phys. Rev. B 15, 1519 (1976) CrossRefADSGoogle Scholar
  9. A. Dutta, B.K. Chakrabarti, R.B. Stinchcombe, J. Phys. A: Math. Gen. 29, 5285 (1996) MATHCrossRefADSGoogle Scholar
  10. C. Kaiser, I. Peschel, J. Phys. A: Math. Gen. 22 4257 (1989) Google Scholar
  11. T. Roscilde, P. Verrucchi, A. Fubini, S. Haas, V. Tognetti, Phys. Rev. Lett. 94, 147208 (2005) CrossRefADSGoogle Scholar
  12. R. Moessner, S.L. Sondhi, P. Chandra, Phys. Rev. Lett. 84, 4457 (2000) CrossRefADSGoogle Scholar
  13. R. Moessner, S.L. Sondhi, Phys. Rev. B 63, 224401 (2001) CrossRefADSGoogle Scholar
  14. G. Stefanucci, M. Cini, Phys. Rev. B 66, 115108 (2002) CrossRefADSGoogle Scholar

Copyright information

© EDP Sciences/Società Italiana di Fisica/Springer-Verlag 2006

Authors and Affiliations

  1. 1.Theoretical Condensed Matter Physics DivisionSaha Institute of Nuclear PhysicsKolkataIndia
  2. 2.Complex Systems Engineering, Graduate School of Information Science and Technology, Hokkaido UniversitySapporoJapan

Personalised recommendations