Emergence of tricritical point and liquid-gas phase in the massless 2+1 dimensional Gross-Neveu model

Physical Review D - Particles, Fields, Gravitation and Cosmology

Volumn 76, Issue 4, 2007, Pages

  Kneur, Jean Loïc ^a   Pinto, Marcus Benghi ^b   Ramos, Rudnei O ^c   Staudt, Ederson ^b  

^a UNIVERSITÉ MONTPELLIER II   (France)

^b FEDERAL UNIVERSITY OF SANTA CATARINA   (Brazil)

^c STATE UNIVERSITY OF RIO DE JANEIRO   (Brazil)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 34548437667     PISSN: 15507998     EISSN: 15502368     Source Type: Journal    
DOI: 10.1103/PhysRevD.76.045020     Document Type: Article

References (65)

1. D. Gross and A. Neveu, Phys. Rev. D 10, 3235 (1974). PRVDAQ 0556-2821 10.1103/PhysRevD.10.3235
2. O. Schnetz, M. Thies, and K. Urlichs, Ann. Phys. (N.Y.) APNYA6 0003-4916 314, 425 (2004); 10.1016/j.aop.2004.06.009
3. M. Thies, J. Phys. A JPHAC5 0305-4470 39, 12707 (2006). 10.1088/0305-4470/39/41/S04
4. A. Chodos and H. Minakata, Nucl. Phys. NUPBBO 0550-3213 B490, 687 (1997). 10.1016/S0550-3213(97)00094-1
5. K.G. Klimenko, Z. Phys. C 37, 457 (1988); ZPCFD2 0170-9739 10.1007/BF01578141
6. B. Rosenstein, S.H. Park, and B.J. Warr, Phys. Rev. D 39, 3088 (1989); PRVDAQ 0556-2821 10.1103/PhysRevD.39.3088
7. B. Rosenstein S.H. Park B.J. Warr Phys. Rev. Lett. 62, 1433 (1989). PRLTAO 0031-9007 10.1103/PhysRevLett.62.1433
8. S. Coleman, Aspects of Symmetry (Cambridge University Press, Cambridge, England, 1985).
9. M. Moshe and J. Zinn-Justin, Phys. Rep. PRPLCM 0370-1573 385, 69 (2003). 10.1016/S0370-1573(03)00263-1
10. U. Wolff, Phys. Lett. 157B, 303 (1985). PHLTAM 0031-9163 10.1016/0370-2693(85)90671-9
11. A. Barducci, R. Casalbuoni, M. Modugno, and G. Pettini, Phys. Rev. D 51, 3042 (1995). PRVDAQ 0556-2821 10.1103/PhysRevD.51.3042
12. N.D. Mermin and H. Wagner, Phys. Rev. Lett. 17, 1133 (1966); PRLTAO 0031-9007 10.1103/PhysRevLett.17.1133
13. S. Coleman, Commun. Math. Phys. 31, 259 (1973); CMPHAY 0010-3616 10.1007/BF01646487
14. L.D. Landau and E.M. Lifshtiz, Statistical Physics (Pergamon, New York, 1958), p. 482.
15. R.F. Dashen, S.-K. Ma, and R. Rajaraman, Phys. Rev. D 11, 1499 (1975). PRVDAQ 0556-2821 10.1103/PhysRevD.11.1499
16. J.B. Kogut and C.G. Strouthos, Phys. Rev. D 63, 054502 (2001). PRVDAQ 0556-2821 10.1103/PhysRevD.63.054502
17. S. Hands, K. Kocic, and J.B. Kogut, Ann. Phys. (N.Y.) APNYA6 0003-4916 224, 29 (1993); 10.1006/aphy.1993.1039
18. S. Hands K. Kocic J.B. Kogut Nucl. Phys. NUPBBO 0550-3213 B390, 355 (1993). 10.1016/0550-3213(93)90460-7
19. J.-L. Kneur, M.B. Pinto, and R.O. Ramos, Phys. Rev. D 74, 125020 (2006); PRVDAQ 0556-2821 10.1103/PhysRevD.74.125020
20. J.-L. Kneur M.B. Pinto R.O. Ramos Braz. J. Phys. 37, 258 (2007). BJPHE6 0103-9733
21. S.K. Gandhi, H.F. Jones, and M.B. Pinto, Nucl. Phys. NUPBBO 0550-3213 B359, 429 (1991). 10.1016/0550-3213(91)90067-8
22. J.-L. Kneur, M.B. Pinto, and R.O. Ramos, Phys. Rev. Lett. 89, 210403 (2002); PRLTAO 0031-9007 10.1103/PhysRevLett.89.210403
23. J.-L. Kneur M.B. Pinto R.O. Ramos Phys. Rev. A 68, 043615 (2003). PLRAAN 1050-2947 10.1103/PhysRevA.68.043615
24. E. Braaten and E. Radescu, Phys. Rev. Lett. 89, 271602 (2002); PRLTAO 0031-9007 10.1103/PhysRevLett.89.271602
25. E. Braaten E. Radescu Phys. Rev. A 66, 063601 (2002). PLRAAN 1050-2947 10.1103/PhysRevA.66.063601
26. J.-L. Kneur, A. Neveu, and M.B. Pinto, Phys. Rev. A 69, 053624 (2004); PLRAAN 1050-2947 10.1103/PhysRevA.69.053624
27. J.-L. Kneur and M.B. Pinto, Phys. Rev. A 71, 033613 (2005); PLRAAN 1050-2947 10.1103/PhysRevA.71.033613
28. B. Kastening, Phys. Rev. A 70, 043621 (2004). PLRAAN 1050-2947 10.1103/PhysRevA.70.043621
29. J.-L. Kneur, M.B. Pinto, R.O. Ramos, and E. Staudt, arXiv:0705.0673.
30. J.I. Kapusta, Finite-Temperature Field Theory (Cambridge University Press, Cambridge, England, 1985);
31. M. Le Bellac, Thermal Field Theory (Cambridge University Press, Cambridge, England, 1996).
32. A. Okopinska, Phys. Rev. D 35, 1835 (1987); PRVDAQ 0556-2821 10.1103/PhysRevD.35.1835
33. M. Moshe and A. Duncan, Phys. Lett. B 215, 352 (1988). PYLBAJ 0370-2693 10.1016/0370-2693(88)91447-5
34. R. Seznec and J. Zinn-Justin, J. Math. Phys. (N.Y.) JMAPAQ 0022-2488 20, 1398 (1979); 10.1063/1.524247
35. J.C. Le Guillou and J. Zinn-Justin, Ann. Phys. (N.Y.) APNYA6 0003-4916 147, 57 (1983); 10.1016/0003-4916(83)90067-2
36. V.I. Yukalov, Moscow University Physics Bulletin MUPBAC 0027-1349 31, 10 (1976);
37. W.E. Caswell, Ann. Phys. (N.Y.) APNYA6 0003-4916 123, 153 (1979); 10.1016/0003-4916(79)90269-0
38. I.G. Halliday and P. Suranyi, Phys. Lett. 85B, 421 (1979); PHLTAM 0031-9163 10.1016/0370-2693(79)91287-5
39. J. Killinbeck, J. Phys. A JPHAC5 0305-4470 14, 1005 (1981); 10.1088/0305-4470/14/5/020
40. R.P. Feynman and H. Kleinert, Phys. Rev. A 34, 5080 (1986); PLRAAN 1050-2947 10.1103/PhysRevA.34.5080
41. H.F. Jones and M. Moshe, Phys. Lett. B 234, 492 (1990); PYLBAJ 0370-2693 10.1016/0370-2693(90)92045-K
42. A. Neveu, Nucl. Phys. B, Proc. Suppl. 18, 242 (1991); NPBSE7 0920-5632 10.1016/0920-5632(91)90137-4
43. V. Yukalov, J. Math. Phys. (N.Y.) JMAPAQ 0022-2488 32, 1235 (1991); 10.1063/1.529320
44. C.M. Bender, Phys. Rev. D 45, 1248 (1992); PRVDAQ 0556-2821 10.1103/PhysRevD.45.1248
45. S. Gandhi and M.B. Pinto, Phys. Rev. D 46, 2570 (1992); PRVDAQ 0556-2821 10.1103/PhysRevD.46.2570
46. H. Yamada, Z. Phys. C 59, 67 (1993); ZPCFD2 0170-9739 10.1007/BF01555840
47. A.N. Sissakian, I.L. Solovtsov, and O.P. Solovtsova, Phys. Lett. B 321, 381 (1994); PYLBAJ 0370-2693 10.1016/0370-2693(94)90262-3
48. H. Kleinert, Phys. Rev. D 57, 2264 (1998); PRVDAQ 0556-2821 10.1103/PhysRevD.57.2264
49. H. Kleinert Phys. Lett. B 434, 74 (1998); PYLBAJ 0370-2693 10.1016/S0370-2693(98)00750-3
50. for a review, see H. Kleinert and V. Schulte-Frohlinde, Critical Properties of 4-Theories (World Scientific, Singapore, 2001), Chap.;
51. K.G. Klimenko, Z. Phys. C 50, 477 (1991); ZPCFD2 0170-9739 10.1007/BF01551460
52. K.G. Klimenko Z. Phys. C 60, 677 (1993); ZPCFD2 0170-9739 10.1007/BF01558396
53. K.G. Klimenko Mod. Phys. Lett. A 9, 1767 (1994); MPLAEQ 0217-7323 10.1142/S0217732394001611
54. M.B. Pinto, R.O. Ramos, and P.J. Sena, Physica A (Amsterdam) 342, 570 (2004). PHYADX 0378-4371 10.1016/j.physa.2004.05.042
55. M.B. Pinto and R.O. Ramos, Phys. Rev. D 60, 105005 (1999); PRVDAQ 0556-2821 10.1103/PhysRevD.60.105005
56. M.B. Pinto R.O. Ramos Phys. Rev. D 61, 125016 (2000). PRVDAQ 0556-2821 10.1103/PhysRevD.61.125016
57. C. Arvanitis, F. Geniet, M. Iacomi, J.-L. Kneur, and A. Neveu, Int. J. Mod. Phys. A 12, 3307 (1997). IMPAEF 0217-751X 10.1142/S0217751X97001730
58. B. Rosenstein, B. Warr, and S.H. Park, Phys. Rep. 205, 59 (1991). PRPLCM 0370-1573 10.1016/0370-1573(91)90129-A
59. J.C. Collins, Renormalization (Cambridge University Press, Cambridge, England, 1984).
60. J. Bijnens, Prog. Part. Nucl. Phys. 58, 521 (2007). PPNPDB 0146-6410 10.1016/j.ppnp.2006.08.002
61. P.M. Stevenson, Phys. Rev. D 23, 2916 (1981); PRVDAQ 0556-2821 10.1103/PhysRevD.23.2916
62. P.M. Stevenson Nucl. Phys. NUPBBO 0550-3213 B203, 472 (1982). 10.1016/0550-3213(82)90325-X
63. R. Root, Phys. Rev. D 11, 831 (1975). PRVDAQ 0556-2821 10.1103/PhysRevD.11.831
64. P. Castorina, M. Mazza, and D. Zappala, Phys. Lett. B 567, 31 (2003). PYLBAJ 0370-2693 10.1016/j.physletb.2003.06.005
65. Handbook of Mathematical Functions, edited by, M. Abramowitz, and, I.A. Stegun, (Dover, New York, 1972), 9th ed..