Quick Search: Journal  Author  Title/Abstract  Vol./Year 

J. Phys. Soc. Jpn. 75 (2006) 014001 (7 pages)  |Previous Article| |Next Article|  |Table of Contents|
|Full Text PDF: OPEN SELECT (125K)|

Gauge Theory for Quantum Spin Glasses

Satoshi Morita, Yukiyasu Ozeki1 and Hidetoshi Nishimori

Department of Physics, Tokyo Institute of Technology, Oh-okayama, Meguro-ku, Tokyo 152-8551
1Department of Applied Physics and Chemistry, The University of Electro-Communications, Chofugaoka, Chofu, Tokyo 182-8585

(Received August 22, 2005; Accepted October 21, 2005; Published December 26, 2005)

The gauge theory for random spin systems is extended to quantum spin glasses to derive a number of exact and/or rigorous results. The transverse Ising model and the quantum gauge glass are shown to be gauge invariant. For these models, an identity is proved that the expectation value of the gauge invariant operator in the ferromagnetic limit is equal to the one in the classical equilibrium state on the Nishimori line. As a result, a set of inequalities for the correlation function are proved, which restrict the location of the ordered phase. It is also proved that there is no long-range order in the two-dimensional quantum gauge glass in the ground state. The phase diagram for the quantum XY Mattis model is determined. ©2006 The Physical Society of Japan

KEYWORDS: spin glass, gauge theory, correlation function, quantum spin system
URL: http://jpsj.ipap.jp/link?JPSJ/75/014001/
DOI: 10.1143/JPSJ.75.014001


|Full Text PDF: OPEN SELECT (125K)|  Citation:

References

  1. K. Binder and A. P. Young: Rev. Mod. Phys. 58 (1986) 801[APS].
  2. K. H. Fischer and J. A. Hertz: Spin Glasses (Cambridge University Press, Cambridge, 1991).
  3. S. F. Edwards and P. W. Anderson: J. Phys. F 5 (1975) 965[IoP STACKS].
  4. D. Sherrington and S. Kirkpatrick: Phys. Rev. Lett. 35 (1975) 1792[APS].
  5. G. Parisi: Phys. Lett. A 73 (1979) 203[CrossRef]; G. Parisi: J. Phys. A 13 (1980); G. Parisi: J. Phys. A (1980) 13 1101[IoP STACKS]; G. Parisi: J. Phys. A 13 (1980) 1887[IoP STACKS]; G. Parisi: J. Phys. A 13 (1980) L115[IoP STACKS].
  6. R. N. Bhatt and A. P. Young: Phys. Rev. Lett. 54 (1985) 924[APS].
  7. A. T. Ogielski and I. Morgenstern: Phys. Rev. Lett. 54 (1985) 928[APS].
  8. R. R. P. Singh and S. Chakravarty: Phys. Rev. Lett. 57 (1986) 245[APS].
  9. R. N. Bhatt and A. P. Young: Phys. Rev. B 37 (1988) 5606[APS].
  10. D. A. Huse and H. S. Seung: Phys. Rev. B 42 (1990) 1059[APS].
  11. J. D. Reger, T. A. Tokuyasu, A. P. Young and M. P. A. Fisher: Phys. Rev. B 44 (1991) 7147[APS].
  12. M. Cieplak, J. R. Banavar and A. Khaurana: J. Phys. A 24 (1991) L145[IoP STACKS].
  13. J. M. Kosterlitz and M. V. Simkin: Phys. Rev. Lett. 79 (1997) 1098[APS].
  14. H. Nishimori and H. Kawamura: J. Phys. Soc. Jpn. 62 (1993) 3266[IPAP].
  15. M. J. P. Gingras: Phys. Rev. B 45 (1992) 7547[APS].
  16. J. D. Reger and A. P. Young: J. Phys. A 26 (1993) L1067[IoP STACKS].
  17. Y.-H. Lie: Phys. Rev. Lett. 69 (1992) 1819[APS].
  18. M. Y. Choi and S. Y. Park: Phys. Rev. B 60 (1999) 4070[APS].
  19. H. Nishimori: Prog. Theor. Phys. 66 (1981) 1169[IPAP].
  20. H. Nishimori: Statistical Physics of Spin Glasses and Information Processing: An Introduction (Oxford University Press, Oxford, 2001).
  21. H. Kitatani: J. Phys. Soc. Jpn. 61 (1992) 4049[IPAP].
  22. Y. Ozeki and H. Nishimori: J. Phys. A 26 (1993) 3399[IoP STACKS].
  23. Y. Ozeki: J. Phys. A 28 (1995) 3645[IoP STACKS]; Y. Ozeki: J. Phys.: Condens. Matter 9 (1997) 11171[IoP STACKS].
  24. Y. Ozeki: J. Phys. A 36 (2003) 2673[IoP STACKS].
  25. J. M. Kosterlitz and D. J. Thouless: J. Phys. C 6 (1973) 1181[IoP STACKS].
  26. T. Kennedy, E. H. Lieb and B. S. Shastry: Phys. Rev. Lett. 61 (1988) 2582[APS].
  27. Y. Ozeki: J. Phys. A 29 (1996) 5805[IoP STACKS].
|TOP|  |Previous Article| |Next Article|  |Table of Contents| |JPSJ Home|
Copyright © 2010 The Physical Society of Japan
Contact Information