Universal spectral correlations of the Dirac operator at finite temperature

Nuclear Physics B

Volumn 506, Issue 3, 1997, Pages 589-611

  Guhr, Thomas ^a   Wettig, Tilo ^a,b  

^a MAX PLANCK INSTITUT FÜR KERNPHYSIK   (Germany)

^b TECHNICAL UNIVERSITY OF MUNICH   (Germany)

Author keywords

Chiral random matrix models; Finite temperature models; Spectrum of the QCD dirac operator

Indexed keywords

EID: 0031521254     PISSN: 05503213     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0550-3213(97)00556-7     Document Type: Article

References (51)

1. [1] M.A. Nowak, J.J.M. Verbaarschot and I. Zahed, Phys. Lett. B 217 (1989) 157.
2. [2] Yu.A. Simonov, Phys. Rev. D 43 (1991) 3534.
3. [3] E.V. Shuryak and J.J.M. Verbaarschot, Nucl. Phys. A 560 (1993) 306.
4. [4] J.J.M. Verbaarschot and I. Zahed, Phys. Rev. Lett. 70 (1993) 3852.
5. [5] J.J.M. Verbaarschot, Nucl. Phys. B 426 [FS] (1994) 559.
6. [6] T. Nagao and K. Slevin, J. Math. Phys. 34 (1993) 2075; T. Nagao and P.J. Forrester, Nucl. Phys. B 435 (1995) 401.
7. [6] T. Nagao and K. Slevin, J. Math. Phys. 34 (1993) 2075; T. Nagao and P.J. Forrester, Nucl. Phys. B 435 (1995) 401.
8. [7] J.J.M. Verbaarschot, Phys. Rev. Lett. 72 (1994) 2531.
9. [8] J.J.M. Verbaarschot, Acta Phys. Pol. B 25 (1994) 133; Nucl. Phys. B 427 (1994) 534.
10. [8] J.J.M. Verbaarschot, Acta Phys. Pol. B 25 (1994) 133; Nucl. Phys. B 427 (1994) 534.
11. [9] J.J.M. Verbaarschot and I. Zahed, Phys. Rev. Lett. 73 (1994) 2288.
12. [10] M.A. Halasz and J.J.M. Verbaarschot, Phys. Rev. Lett. 74 (1995) 3920; M.A. Halasz, T. Kalkreuter and J.J.M. Verbaarschot, Nucl. Phys. B (Proc. Suppl.) 53 (1997) 266.
13. [10] M.A. Halasz and J.J.M. Verbaarschot, Phys. Rev. Lett. 74 (1995) 3920; M.A. Halasz, T. Kalkreuter and J.J.M. Verbaarschot, Nucl. Phys. B (Proc. Suppl.) 53 (1997) 266.
14. [11] A. Smilga and J.J.M. Verbaarschot, Phys. Rev. D 51 (1995) 829.
15. [12] M.A. Halasz and J.J.M. Verbaarschot, Phys. Rev. D 52 (1995) 2563.
16. [13] J.J.M. Verbaarschot, Phys. Lett. B 368 (1996) 137.
17. [14] A.D. Jackson and J.J.M. Verbaarschot, Phys. Rev. D 53 ( 1996) 7223.
18. [15] T. Wettig, A. Schäfer and H.A. Weidenmüller, Phys. Lett. B 367 (1996) 28.
19. [16] M.A. Stephanov, Phys. Lett. B 375 (1996) 249.
20. [17] M.A. Stephanov, Phys. Rev. Lett. 76 (1996) 4472.
21. [18] J. Jurkiewicz, M.A. Nowak and I. Zahed, Nucl. Phys. B 478 (1996) 605; M.A. Nowak, G. Papp and I. Zahed, Phys. Lett. B 389 (1996) 137, 341; R.A. Janik, M.A. Nowak and I. Zahed, Phys. Lett. B 392 ( 1997) 155.
22. [18] J. Jurkiewicz, M.A. Nowak and I. Zahed, Nucl. Phys. B 478 (1996) 605; M.A. Nowak, G. Papp and I. Zahed, Phys. Lett. B 389 (1996) 137, 341; R.A. Janik, M.A. Nowak and I. Zahed, Phys. Lett. B 392 ( 1997) 155.
23. [18] J. Jurkiewicz, M.A. Nowak and I. Zahed, Nucl. Phys. B 478 (1996) 605; M.A. Nowak, G. Papp and I. Zahed, Phys. Lett. B 389 (1996) 137, 341; R.A. Janik, M.A. Nowak and I. Zahed, Phys. Lett. B 392 ( 1997) 155.
24. [19] A.D. Jackson, M.K. Şener and J.J.M. Verbaarschot, Nucl. Phys. B 479 (1996) 707.
25. [20] A.D. Jackson, M.K. Şener and J.J.M. Verbaarschot, Phys. Lett. B 387 (1996) 355.
26. [21] J.J.M. Verbaarschot, in: Proceedings of the 2nd Workshop on Continuous Advances in QCD, Minneapolis 1996, pp. 325-337, hep-lat/9606009; Nucl. Phys. B (Proc. Suppl.) 53 (1997) 88.
27. [21] J.J.M. Verbaarschot, in: Proceedings of the 2nd Workshop on Continuous Advances in QCD, Minneapolis 1996, pp. 325-337, hep-lat/9606009; Nucl. Phys. B (Proc. Suppl.) 53 (1997) 88.
28. [22] O. Bohigas and M.J. Giannoni, Lecture Notes in Physics 209 (Springer, Heidelberg, 1984).
29. [23] M.L. Mehta, Random Matrices, 2nd Ed. (Academic Press, New York, 1991).
30. [24] F. Haake, Quantum Signatures of Chaos (Springer, Berlin, 1991).
31. [25] T. Banks and A. Casher, Nucl. Phys. B 169 (1980) 103.
32. [26] H. Leutwyler and A. Smilga, Phys. Rev. D 46 (1992) 5607.
33. [27] K. Slevin and T. Nagao, Phys. Rev. Lett, 70 (1993) 635.
34. [28] E. Brézin, S. Hikami and A. Zee, Nucl. Phys. B 464 (1996) 411; S. Nishigaki, Phys. Lett. B 387 (1996) 139.
35. [28] E. Brézin, S. Hikami and A. Zee, Nucl. Phys. B 464 (1996) 411; S. Nishigaki, Phys. Lett. B 387 (1996) 139.
36. [29] G. Akemann, P.H. Damgaard, U. Magnea and S. Nishigaki, Nucl. Phys. B 487 (1997) 721.
37. [30] M.E. Berbenni-Bitsch, S. Meyer, A. Schäfer, J.J.M. Verbaarschot and T. Wettig, hep-lat/9704018.
38. [31] F.J. Dyson, J. Math. Phys. 3 (1962) 140, 157, 166, 1199.
39. [32] T. Guhr and T. Wettig, J. Math. Phys. 37 (1996) 6395.
40. [33] E.P. Wigner, Ann. Math. 53 (1951) 36.
41. [34] K.B. Efetov, Adv. Phys. 32 ( 1983) 53.
42. [35] J.J.M. Verbaarschot, H.A. Weidenmüller, and M. Zimbauer, Phys. Rep. 129 (1985) 367.
43. [36] T. Guhr, Phys. Rev. Lett. 76 (1996) 2258; Ann. Phys. (NY) 250 ( 1996) 145.
44. [36] T. Guhr, Phys. Rev. Lett. 76 (1996) 2258; Ann. Phys. (NY) 250 ( 1996) 145.
45. [37] T. Guhr, J. Math. Phys. 32 (1991) 336.
46. [38] M. Abramowitz and I.A. Stegun, Handbook of Mathematical Functions (Dover, New York, 1972).
47. [39] See, e.g., R.A. Janik, M.A. Nowak, G. Papp, and I. Zahed, Phys. Rev. Lett. 77 (1996) 4876; R.A. Janik, M.A. Nowak, G. Papp, J. Wambach and I. Zahed, Phys. Rev. E 55 (1997) 4100; J. Feinberg and A. Zee, cond-mat/9703087; M.A. Halasz, A.D. Jackson and J.J.M. Verbaarschot, hep-lat/9703006, to appear in Phys. Rev. D 56, Vol. 8 (15 Oct. 1997).
48. [39] See, e.g., R.A. Janik, M.A. Nowak, G. Papp, and I. Zahed, Phys. Rev. Lett. 77 (1996) 4876; R.A. Janik, M.A. Nowak, G. Papp, J. Wambach and I. Zahed, Phys. Rev. E 55 (1997) 4100; J. Feinberg and A. Zee, cond-mat/9703087; M.A. Halasz, A.D. Jackson and J.J.M. Verbaarschot, hep-lat/9703006, to appear in Phys. Rev. D 56, Vol. 8 (15 Oct. 1997).
49. [39] See, e.g., R.A. Janik, M.A. Nowak, G. Papp, and I. Zahed, Phys. Rev. Lett. 77 (1996) 4876; R.A. Janik, M.A. Nowak, G. Papp, J. Wambach and I. Zahed, Phys. Rev. E 55 (1997) 4100; J. Feinberg and A. Zee, cond-mat/9703087; M.A. Halasz, A.D. Jackson and J.J.M. Verbaarschot, hep-lat/9703006, to appear in Phys. Rev. D 56, Vol. 8 (15 Oct. 1997).
50. [39] See, e.g., R.A. Janik, M.A. Nowak, G. Papp, and I. Zahed, Phys. Rev. Lett. 77 (1996) 4876; R.A. Janik, M.A. Nowak, G. Papp, J. Wambach and I. Zahed, Phys. Rev. E 55 (1997) 4100; J. Feinberg and A. Zee, cond-mat/9703087; M.A. Halasz, A.D. Jackson and J.J.M. Verbaarschot, hep-lat/9703006, to appear in Phys. Rev. D 56, Vol. 8 (15 Oct. 1997).
51. [40] A.D. Jackson, M.K. Şener and J.J.M. Verbaarschot, Nucl. Phys. B 506 (1997) 612, next paper in this issue, hep-th/9704056.