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Thermodynamics of the Gross-Neveu model beyond the mean-field approximation

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References

  1. For a review of the current status of heavy-ion collisions see, e.g., Singh C. P., Phys. Rep., 236 (1993) 147

    Article  ADS  Google Scholar 

  2. Tserruya I., Brussels EPS HEP, (1995) 841

    Google Scholar 

  3. Harris J. W. and Müller B., Ann. Rev. Nucl. Part. Sci., 46 (1996) 71.

    Article  ADS  Google Scholar 

  4. Barnet R. M. et al., Phys. Rev. D, 54 (1996) 1, and 1997 off-year partial update for the 1998 edition (URL://pdg.lbl.gov).

    Article  ADS  Google Scholar 

  5. Barducci A., Casalbuoni R., De Curtis S., Gatto R. and Pettini G., Phys. Lett. B, 244 (1990) 311.

    Article  ADS  Google Scholar 

  6. Gasser J. and Leutwyler H., Phys. Lett. B, 184 (1987) 83; 188 (1987) 477

    Article  ADS  Google Scholar 

  7. Gerber P. and Leutwyler H., Nucl. Phys. B, 321 (1989) 387.

    Article  ADS  Google Scholar 

  8. Barducci A., Casalbuoni R., De Curtis S., Gatto R. and Pettini G., Phys. Rev. D, 41 (1990) 1610, and references therein.

    Article  ADS  Google Scholar 

  9. Leutwyler H., Phys. Lett. B, 284 (1992) 106

    Article  ADS  Google Scholar 

  10. Barducci A., Casalbuoni R., Pettini G. and Gatto R., Phys. Lett. B, 301 (1993) 95.

    Article  ADS  Google Scholar 

  11. Pisarski R. D., preprint hep-ph/9503330 and references therein.

  12. Brown G. E. and Rho M., Phys. Rep., 269 (1996) 333, and references therein.

    Article  ADS  Google Scholar 

  13. Nambu Y. and Jona- Lasinio G., Phys. Rev., 122 (1961) 345; 124 (1961) 246.

    Article  ADS  Google Scholar 

  14. Gross D. J. and Neveu A., Phys. Rev. D, 10 (1974) 3235.

    Article  ADS  Google Scholar 

  15. For a recent review on the NJL model and its applications to QCD see, e.g., Vogl U. and Weise W., Prog. Part. Nucl. Phys., 27 (1991) 195

    Article  ADS  Google Scholar 

  16. Klevansky S. P., Rev. Mod. Phys., 64 (1992) 649.

    Article  ADS  MathSciNet  Google Scholar 

  17. Hüfner J., Klevansky S. P., Zhuang P. and Voss H., Ann. Phys., 234 (1994) 225

    Article  ADS  Google Scholar 

  18. Zhuang P., Hüfner J., and Klevansky S. P., Nucl. Phys. A, 576 (1994) 525.

    Article  ADS  Google Scholar 

  19. Dmitrasinović V., Schulze H. J., Tegen R. and Lemmer R. H., Ann. Phys., 238 (1994) 332

    Article  ADS  Google Scholar 

  20. Nikolov E. N., Broniowski W., Christov C. V., Ripka G. and Goeke K., Nucl. Phys. A, 608 (1996) 411

    Article  ADS  Google Scholar 

  21. de Mello Kock R. and Rodrigues J. P., Phys. Rev. D, 54 (1996) 7794.

    Article  ADS  Google Scholar 

  22. Blaschke D., Kalinovskii Y. L., Roepke G., Schmidt S. and Volkov M. K., Phys. Rev. C, 53 (1996) 2394

    Article  ADS  Google Scholar 

  23. Florkowski W. and Broniowski W., Phys. Lett. B, 386 (1996) 62.

    Article  ADS  Google Scholar 

  24. Barducci A., Casalbuoni R., Gatto R., Modugno M. and Pettini G., Mod. Phys. Lett. A, 11 (1996) 1579.

    Article  ADS  Google Scholar 

  25. Barducci A., Casalbuoni R., Gatto R., Modugno M. and Pettini G., Phys. Rev. D, 55 (1997) 2247.

    Article  ADS  Google Scholar 

  26. Gatto R., Modugno M. and Pettini G., Phys. Rev. D, 57 (1998) 4995.

    ADS  Google Scholar 

  27. Esposito E. P., Shovkovy I. A. and Wijewardhana L. C. R., Phys. Rev. D, 58 (1998) 065003.

    Article  ADS  Google Scholar 

  28. For a discussion of the 1/N expansion see, e.g., Coleman S., in Aspects of Symmetry (Cambridge University Press, Cambridge) 1988, p. 351

    Google Scholar 

  29. Zinn-Justin J., in Quantum Field Theory and CriticalPhenomena (Oxford University Press, Oxford) 1989, p. 635.

    Google Scholar 

  30. Gross D. J., in Methods in Field Theory, edited by R. Balian and J. Zinn-Justin (North-Holland, Amsterdam) 1976.

  31. Berezinski V. L., Sov. Phys. JETP, 32 (1971) 493

    ADS  Google Scholar 

  32. Kosterlitz J. M. and Thouless D. J., J. Phys. C, 6 (1973) 1181.

    Article  ADS  Google Scholar 

  33. Mermin N. D. and Wagner H., Phys. Rev. Lett., 17 (1966) 1133.

    Article  ADS  Google Scholar 

  34. Coleman S., Commun. Math. Phys., 31 (1973) 259.

    Article  ADS  Google Scholar 

  35. For a review of finite-temperature field theory methods see, e.g., Landsman N. P. and van Weert Ch. G., Phys. Rep., 145 (1987) 141

    Article  ADS  MathSciNet  Google Scholar 

  36. Kapusta J. I., in Finite Temperature Field Theory (Cambridge University Press) 1989

    MATH  Google Scholar 

  37. Altherr T., Int. J. Mod. Phys. A, 8 (1993) 5605.

    Article  ADS  MathSciNet  Google Scholar 

  38. See, e.g., Zinn-Justin J., in Quantum Field Theory and Critical Phenomena (Clarendon Press, Oxford) 1989

    MATH  Google Scholar 

  39. Parisi G., in StatisticalField Theory (Addison-Wesley) 1988

    Google Scholar 

  40. Goldenfeld N., in Lectures on Phase Transitions and the Renormalization Group (Addison-Wesley) 1992.

    MATH  Google Scholar 

  41. See, e.g., Muta T., in Foundations of QCD (World Scientific) 1986.

    Google Scholar 

  42. Kadanoff L. P. and Baym G., in Quantum StatisticalMechanics (Benjamin, New York) 1962.

    MATH  Google Scholar 

  43. ’t Hooft G., Phys. Rev. Lett., 37 (8) 1976; Phys. Rev. D, 14 (1976) 3432.

    Article  ADS  Google Scholar 

  44. Jackiw R., Phys. Rev. D, 9 (1974) 1686.

    Article  ADS  Google Scholar 

  45. Bocharev A. I. and Shaposhnikov M. E., Nucl. Phys. B, 268 (1986) 220

    Article  ADS  Google Scholar 

  46. Dominguez C. A. and Loewe M., Phys. Lett. B, 233 (1989) 201.

    Article  ADS  Google Scholar 

  47. Jacobs L., Phys. Rev. D, 10 (1974) 3956

    Article  ADS  Google Scholar 

  48. Harrington B. and Yildiz A., Phys. Rev. D, 11 (1975) 779.

    Article  ADS  Google Scholar 

  49. Root R. G., Phys. Rev. D, 11 (1975) 831.

    Article  ADS  Google Scholar 

  50. Schonfeld F., Nucl. Phys. B, 95 (1975) 148.

    Article  ADS  Google Scholar 

  51. Dashen R. F., Ma S. K. and Rajaraman R., Phys. Rev. D, 11 (1975) 1499.

    Article  ADS  Google Scholar 

  52. Parisi G., Nucl. Phys. B, 100 (1975) 368

    Article  ADS  Google Scholar 

  53. Shizuya K., Phys. Rev. D, 21 (1980) 2327.

    Article  ADS  Google Scholar 

  54. Witten E., Nucl. Phys. B, 145 (1978) 110.

    Article  ADS  Google Scholar 

  55. Haymaker R. W. and Cooper F., Phys. Rev. D, 19 (1979) 562.

    Article  ADS  Google Scholar 

  56. Cohen Y., Elitzur S. and Rabinovici E., Nucl. Phys. B, 220 (1983) 102.

    Article  ADS  Google Scholar 

  57. Wolff U., Phys. Lett. B, 157 (1985) 303.

    Article  ADS  Google Scholar 

  58. Karsch F., Kogut J. and Wyld H. W., Nucl. Phys. B, 280 (1987) 289.

    Article  ADS  Google Scholar 

  59. Klimenko K. G., Theor. Math. Phys., 75 (1988) 487.

    Article  Google Scholar 

  60. Klimenko K. G., Z. Phys. C, 37 (1988) 457.

    Article  ADS  Google Scholar 

  61. Treml T. F., Phys. Rev. D, 39 (1989) 679.

    Article  ADS  Google Scholar 

  62. Rosenstein B., Warr B. J. and Park S. H., Phys. Rep., 205 (1991) 59.

    Article  ADS  Google Scholar 

  63. Huang S., Phys. Rev. D, 47 (1993) 653.

    Article  ADS  Google Scholar 

  64. Barducci A., Casalbuoni R., Gatto R., Modugno M. and Pettini G., Phys. Rev. D, 51 (1995) 3042.

    Article  ADS  Google Scholar 

  65. See, e.g., Davis A. C. and Matheson A. M., Nucl. Phys. B, 258 (1985) 373 and references therein.

    Article  ADS  Google Scholar 

  66. Olver F. W., in Asymptotics and SpecialFunctions (Academic Press) 1974.

    Google Scholar 

  67. See, e.g., Lawrie I. D. and Sarbach S., in Phase Transitions and CriticalPhenomena edited by C. Domb and J. L. Lebowitz, Vol. 9 (Academic Press) 1984, pp. 1, 155.

  68. Rosenstein B. and Warr B. J., Phys. Lett. B, 218 (465) 1989.

    Article  ADS  Google Scholar 

  69. He H. J., Kuang Y. P., Wang Q. and Yi Y. P., Phys. Rev. D, 45 (1992) 4610.

    Article  ADS  Google Scholar 

  70. See, e.g., Appelquist T. W., Bowick M., Karabali D. and Wijewardhana L. C. R., Phys. Rev. D, 33 (1986) 3704.

    Article  ADS  Google Scholar 

  71. Okopińska A., Phys. Rev. D, 38 (1988) 2507

    Article  ADS  Google Scholar 

  72. Klimenko K. G., Z. Phys. C, 37 (1988) 457; 54 (323) 1992

    Article  ADS  Google Scholar 

  73. Klimenko K. G., Magnitskii B. V. and Vshivtsev A. S., Nuovo Cimento A, 107 (1994) 439

    Article  ADS  Google Scholar 

  74. Inagaki T., in Thermal Field Theories and Their Applications, edited by Y. X. Gui, F. C. Khanna and Z. B. Su (World Scientific) 1996.

  75. Rosenstein B., Warr B. J. and Park S. H., Phys. Rev. D, 39 (1989) 3088.

    Article  ADS  Google Scholar 

  76. Shen Kun and Qui Zhongping, Phys. Rev. D, 45 (1992) 3877; 48 (1993) 1801.

    Article  MathSciNet  Google Scholar 

  77. Gat G., Kovner A., Rosenstein B. and Warr B. J., Phys. Lett. B, 240 (1990) 158.

    Article  ADS  Google Scholar 

  78. Weinberg E. J. and Wu A., Phys. Rev. D, 36 (1987) 2474.

    Article  ADS  MathSciNet  Google Scholar 

  79. Rehberg P. and Klevansky S. P., Ann. Phys., 252 (1996) 422.

    Article  ADS  Google Scholar 

  80. Lewin L., in Polylogarithms and Associated Functions (North Holland) 1981.

    MATH  Google Scholar 

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Modugno, M. Thermodynamics of the Gross-Neveu model beyond the mean-field approximation. Riv. Nuovo Cim. 23, 1–67 (2000). https://doi.org/10.1007/BF03548885

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