Anti-ferromagnetic condensate in Yang-Mills theory

Nuclear Physics B

Volumn 486, Issue 1-2, 1997, Pages 315-336

  Fingberg, Jochen ^a   Polonyi, Janos ^b,c  

^a UNIVERSITY OF WUPPERTAL   (Germany)

^b UNIVERSITÉ DE STRASBOURG   (France)

^c EÖTVÖS LORÁND UNIVERSITY   (Hungary)

Author keywords

Anti ferromagnetic; Competing interactions; Higher order derivatives; Non Abelian gauge theories; Vacuum

Indexed keywords

EID: 0031575474     PISSN: 05503213     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0550-3213(96)00649-9     Document Type: Article

References (91)

1. [1] K.G. Wilson and J. Kogut, Phys. Rep. 12C (1974) 75; K.G. Wilson and Rev. Mod. Phys. 47 (1975) 773; Rev. Mod. Phys. 55 (1983) 583.
2. [1] K.G. Wilson and J. Kogut, Phys. Rep. 12C (1974) 75; K.G. Wilson and Rev. Mod. Phys. 47 (1975) 773; Rev. Mod. Phys. 55 (1983) 583.
3. [1] K.G. Wilson and J. Kogut, Phys. Rep. 12C (1974) 75; K.G. Wilson and Rev. Mod. Phys. 47 (1975) 773; Rev. Mod. Phys. 55 (1983) 583.
4. [2] A. Hasenfratz and P. Hasenfratz, Ann. Rev. Nucl. Part. Sci. 35 (1985) 559.
5. [3] S.B. Liao and J. Polonyi, Phys. Rev. D 51 (1955) 4474.
6. [4] P.I. Fomin, V.P. Gusynin and V.A. Miranskii, Phys. Rev. 78B (1978) 136; V.A. Miranskii, Phys. Lett. 91B (1980) 421; Nucl. Phys. 90A (1985) 149; V.A. Miranskii, Dynamical Symmetry Breaking in Quantum Field Theories (World Scientific, Singapore, 1994).
7. [4] P.I. Fomin, V.P. Gusynin and V.A. Miranskii, Phys. Rev. 78B (1978) 136; V.A. Miranskii, Phys. Lett. 91B (1980) 421; Nucl. Phys. 90A (1985) 149; V.A. Miranskii, Dynamical Symmetry Breaking in Quantum Field Theories (World Scientific, Singapore, 1994).
8. [4] P.I. Fomin, V.P. Gusynin and V.A. Miranskii, Phys. Rev. 78B (1978) 136; V.A. Miranskii, Phys. Lett. 91B (1980) 421; Nucl. Phys. 90A (1985) 149; V.A. Miranskii, Dynamical Symmetry Breaking in Quantum Field Theories (World Scientific, Singapore, 1994).
9. [4] P.I. Fomin, V.P. Gusynin and V.A. Miranskii, Phys. Rev. 78B (1978) 136; V.A. Miranskii, Phys. Lett. 91B (1980) 421; Nucl. Phys. 90A (1985) 149; V.A. Miranskii, Dynamical Symmetry Breaking in Quantum Field Theories (World Scientific, Singapore, 1994).
10. [5] C.N. Leung, S.T. Love and W.A. Bardeen, Nucl. Phys. B 273 (1986) 649.
11. [6] S. Caracciolo, R.G. Edwards, A. Pelissetto and A.D. Sokal, Nucl. Phys. B 30 (Proc. Suppl.) (1993) 815.
12. [7] H.G. Ballesteros, L.A. Fernández, V. Martin-Mayor and A. Munoz Sudupe, Phys. Lett. B 378 (1996) 207.
13. [8] M. Hasenbusch, Phys. Rev. D 53 (1996) 3445.
14. n and O(n) Lattice Sigma Models, e-Print Archive: hep-lat/9507005.
15. [10] C. Frick and J. Jersák, Phys. Rev. D 52 (1995) 340; E. Focht, J. Jersák and J. Paul, Magnetic and chiral universality classes in a 3D Yukawa model, e-Print Archive: hep-lat/9509040.
16. [10] C. Frick and J. Jersák, Phys. Rev. D 52 (1995) 340; E. Focht, J. Jersák and J. Paul, Magnetic and chiral universality classes in a 3D Yukawa model, e-Print Archive: hep-lat/9509040.
17. [11] H. Neuberger, University of Tel-Aviv thesis (1976); M. Bander, Univ. Calif. Irvine, Preprint (1975); M. Halpern, Phys. Rev. D 12 (1975) 1684; H. Lehmann and J. Stehr, The Bose Field Structure associated with a free massive Dirac Field in one space Dimension, DESY Preprint, 76/29, June 1976; B. Schroer and T. Truong, Phys. Rev. D 15 (1977) 1684.
18. [11] H. Neuberger, University of Tel-Aviv thesis (1976); M. Bander, Univ. Calif. Irvine, Preprint (1975); M. Halpern, Phys. Rev. D 12 (1975) 1684; H. Lehmann and J. Stehr, The Bose Field Structure associated with a free massive Dirac Field in one space Dimension, DESY Preprint, 76/29, June 1976; B. Schroer and T. Truong, Phys. Rev. D 15 (1977) 1684.
19. [11] H. Neuberger, University of Tel-Aviv thesis (1976); M. Bander, Univ. Calif. Irvine, Preprint (1975); M. Halpern, Phys. Rev. D 12 (1975) 1684; H. Lehmann and J. Stehr, The Bose Field Structure associated with a free massive Dirac Field in one space Dimension, DESY Preprint, 76/29, June 1976; B. Schroer and T. Truong, Phys. Rev. D 15 (1977) 1684.
20. [11] H. Neuberger, University of Tel-Aviv thesis (1976); M. Bander, Univ. Calif. Irvine, Preprint (1975); M. Halpern, Phys. Rev. D 12 (1975) 1684; H. Lehmann and J. Stehr, The Bose Field Structure associated with a free massive Dirac Field in one space Dimension, DESY Preprint, 76/29, June 1976; B. Schroer and T. Truong, Phys. Rev. D 15 (1977) 1684.
21. [11] H. Neuberger, University of Tel-Aviv thesis (1976); M. Bander, Univ. Calif. Irvine, Preprint (1975); M. Halpern, Phys. Rev. D 12 (1975) 1684; H. Lehmann and J. Stehr, The Bose Field Structure associated with a free massive Dirac Field in one space Dimension, DESY Preprint, 76/29, June 1976; B. Schroer and T. Truong, Phys. Rev. D 15 (1977) 1684.
22. [12] K. Huang and J. Polonyi, J. Mod. Phys. A 6 (1991) 409.
23. [13] T. Reisz, Comm. Math. Phys. 116 (1988) 81, 573; 117 (1988) 79; Nucl. Phys. B 318 (1989) 417.
24. [13] T. Reisz, Comm. Math. Phys. 116 (1988) 81, 573; 117 (1988) 79; Nucl. Phys. B 318 (1989) 417.
25. [13] T. Reisz, Comm. Math. Phys. 116 (1988) 81, 573; 117 (1988) 79; Nucl. Phys. B 318 (1989) 417.
26. [14] J. Zinn-Justin, Quantum Field Theory and Critical Phenomena (Clarendon Press, Oxford, 1979).
27. [15] T.D. Bakeyev and A.A. Slavnov, Higher Covariant Derivative Regularization Revisited, e-Print Archive: hep-th/9601092.
28. [16] T. Appelquist and J. Carazzone, Phys. Rev. D 11 (1975) 2856; T. Appelquist, J. Carazzone, H. Kluberg-Stern and M. Roth, Phys. Rev. Lett. 36 (1976) 768, 1161; T. Appelquist and J. Carazzone, Nucl. Phys. B 120 (1977) 77.
29. [16] T. Appelquist and J. Carazzone, Phys. Rev. D 11 (1975) 2856; T. Appelquist, J. Carazzone, H. Kluberg-Stern and M. Roth, Phys. Rev. Lett. 36 (1976) 768, 1161; T. Appelquist and J. Carazzone, Nucl. Phys. B 120 (1977) 77.
30. [16] T. Appelquist and J. Carazzone, Phys. Rev. D 11 (1975) 2856; T. Appelquist, J. Carazzone, H. Kluberg-Stern and M. Roth, Phys. Rev. Lett. 36 (1976) 768, 1161; T. Appelquist and J. Carazzone, Nucl. Phys. B 120 (1977) 77.
31. [17] V. Branchina, J. Polonyi, Nucl. Phys. B 433 (1995) 99.
32. [18] M. Lüscher, Nucl. Phys. B 200 (1982) 61; J. Polonyi, Phys. Rev. D 29 (1984) 716.
33. [18] M. Lüscher, Nucl. Phys. B 200 (1982) 61; J. Polonyi, Phys. Rev. D 29 (1984) 716.
34. [19] Y. Iwasaki and T. Yoshie, Phys. Lett. 130B (1983) 77; S. Itoh, Y. Iwasaki and T. Yoshie, Phys. Lett. 147B ( 1984) 141.
35. [19] Y. Iwasaki and T. Yoshie, Phys. Lett. 130B (1983) 77; S. Itoh, Y. Iwasaki and T. Yoshie, Phys. Lett. 147B ( 1984) 141.
36. [20] M. Lüscher, Comm. Math. Phys. 85 (1982) 39; A. Phillips and D. Stone, Comm. Math. Phys. 103 (1986) 599; J. Hoek, M. Teper and J. Waterhouse, Nucl. Phys. B 288 (1987) 589.
37. [20] M. Lüscher, Comm. Math. Phys. 85 (1982) 39; A. Phillips and D. Stone, Comm. Math. Phys. 103 (1986) 599; J. Hoek, M. Teper and J. Waterhouse, Nucl. Phys. B 288 (1987) 589.
38. [20] M. Lüscher, Comm. Math. Phys. 85 (1982) 39; A. Phillips and D. Stone, Comm. Math. Phys. 103 (1986) 599; J. Hoek, M. Teper and J. Waterhouse, Nucl. Phys. B 288 (1987) 589.
39. [21] L.S. Schulman, Techiques and Applications of Path Integration (Addison-Wesley, New York, 1981 ).
40. [22] J. Polonyi, Renormalization Group in Quantum Mechanics, Nucl. Phys. B 42 (Proc. Suppl.) (1995) 926.
41. [23] J. Polonyi, Contribution to Workshop on Quantum Infrared Physics, Paris, France, 6-10 June 1994, e-Print Archive: hep-th/9411215.
42. [24] P. Hasenfratz and F. Niedermayer, Nucl. Phys. B 414 (1994) 785; T. DeGrand, A. Hasenfratz, P. Hasenfratz and F. Niedermayer, Nucl. Phys. B 454 (1995) 587.
43. [24] P. Hasenfratz and F. Niedermayer, Nucl. Phys. B 414 (1994) 785; T. DeGrand, A. Hasenfratz, P. Hasenfratz and F. Niedermayer, Nucl. Phys. B 454 (1995) 587.
44. [25] M. Lüscher and P. Weisz, Comm. Math. Phys. 97 (1985) 59;
45. [98 (1985) 443E].
46. [26] C.J. Morningstar, Phys. Rev. D 48 (1993) 2265.
47. [27] M. García Pérez, A. Gonzáles-Arroyo, J. Snippe and P. van Baal, Nucl. Phys. B 413 (1994) 535; M. García Pérez, J. Snippe and P. van Baal, Testing Improved Actions, e-Print Archive: hep-lat/9607007.
48. [27] M. García Pérez, A. Gonzáles-Arroyo, J. Snippe and P. van Baal, Nucl. Phys. B 413 (1994) 535; M. García Pérez, J. Snippe and P. van Baal, Testing Improved Actions, e-Print Archive: hep-lat/9607007.
49. [28] B. Beinlich, F. Karsch and E. Laermann, Nucl. Phys. B 462 (1996) 415.
50. [29] K. Symanzik, Nucl. Phys. B 226 (1983) 187, 205.
51. [30] M. Lüscher and P. Weisz, Phys. Lett. B 158 (1985) 250.
52. [31] W. Selke, in Phase Transitions and Critical Phenomena, ed. C. Domb and J.L. Lebowitz (Academic Press, London, 1992).
53. [32] J.L. Alonso, et al., Non-classical exponents in the d = 4 Ising model with two couplings, hep-lat/9503016, to appear in Phys. Lett. B; I. Campos, L.A. Fernandez and A. Tarancon, Antiferromagnetic 4D O(4) Model, hep-lat/9606017, accepted for publication in Phys. Rev. D.
54. [32] J.L. Alonso, et al., Non-classical exponents in the d = 4 Ising model with two couplings, hep-lat/9503016, to appear in Phys. Lett. B; I. Campos, L.A. Fernandez and A. Tarancon, Antiferromagnetic 4D O(4) Model, hep-lat/9606017, accepted for publication in Phys. Rev. D.
55. [33] G. Parisi and J.J. Ruiz-Lorenzo, J. Phys. A: Math. and Gen. 28 (1995) L395.
56. [34] S. Caracciolo and S. Paternello, Phys. Lett. A 126 (1988) 233; M. Bernashi et al., Phys. Lett. B 231 (1989) 157; L.A. Fernandez et al., Phys. Lett. B 217 (1989) 314; R.V. Gavai and F. Karsch, Phys. Rev. B 46 (1992) 944; S.J. Ferreira and A.D. Sokal, Antiferromagnetic Potts Model on the Square Lattice, e-Print Archive: hep-lat/9405015.
57. [34] S. Caracciolo and S. Paternello, Phys. Lett. A 126 (1988) 233; M. Bernashi et al., Phys. Lett. B 231 (1989) 157; L.A. Fernandez et al., Phys. Lett. B 217 (1989) 314; R.V. Gavai and F. Karsch, Phys. Rev. B 46 (1992) 944; S.J. Ferreira and A.D. Sokal, Antiferromagnetic Potts Model on the Square Lattice, e-Print Archive: hep-lat/9405015.
58. [34] S. Caracciolo and S. Paternello, Phys. Lett. A 126 (1988) 233; M. Bernashi et al., Phys. Lett. B 231 (1989) 157; L.A. Fernandez et al., Phys. Lett. B 217 (1989) 314; R.V. Gavai and F. Karsch, Phys. Rev. B 46 (1992) 944; S.J. Ferreira and A.D. Sokal, Antiferromagnetic Potts Model on the Square Lattice, e-Print Archive: hep-lat/9405015.
59. [34] S. Caracciolo and S. Paternello, Phys. Lett. A 126 (1988) 233; M. Bernashi et al., Phys. Lett. B 231 (1989) 157; L.A. Fernandez et al., Phys. Lett. B 217 (1989) 314; R.V. Gavai and F. Karsch, Phys. Rev. B 46 (1992) 944; S.J. Ferreira and A.D. Sokal, Antiferromagnetic Potts Model on the Square Lattice, e-Print Archive: hep-lat/9405015.
60. [34] S. Caracciolo and S. Paternello, Phys. Lett. A 126 (1988) 233; M. Bernashi et al., Phys. Lett. B 231 (1989) 157; L.A. Fernandez et al., Phys. Lett. B 217 (1989) 314; R.V. Gavai and F. Karsch, Phys. Rev. B 46 (1992) 944; S.J. Ferreira and A.D. Sokal, Antiferromagnetic Potts Model on the Square Lattice, e-Print Archive: hep-lat/9405015.
61. [35] G. Gallavotti and V. Rivasseau, Phys. Lett. 122B (1983) 268.
62. [36] K. Osterwalder and R. Schrader, Comm. Math. Phys. 31 (1973) 83; K. Osterwalder end E. Seiler, Ann. Phys. 110 (1978) 440.
63. [36] K. Osterwalder and R. Schrader, Comm. Math. Phys. 31 (1973) 83; K. Osterwalder end E. Seiler, Ann. Phys. 110 (1978) 440.
64. [37] A. Pais and G.E. Uhlenbeck, Phys. Rev. 79 (1950) 145.
65. [38] T.D. Lee and G.C. Wick, Nucl. Phys. B 9 (1969) 209; Phys. Rev. D 2 (1970) 1033.
66. [38] T.D. Lee and G.C. Wick, Nucl. Phys. B 9 (1969) 209; Phys. Rev. D 2 (1970) 1033.
67. [39] C. Liu, K. Jansen and J. Kuti, Nucl. Phys. B 34 (Proc. Suppl.) (1994) 635; Nucl. Phys. B 42 (Proc. Suppl.) (1995) 630.
68. [39] C. Liu, K. Jansen and J. Kuti, Nucl. Phys. B 34 (Proc. Suppl.) (1994) 635; Nucl. Phys. B 42 (Proc. Suppl.) (1995) 630.
69. [40] Chung-I Tan and Zai-Xin Xi, Phys. Rev. D 30 ( 1984) 455.
70. [41] M. Nauenberg and B. Nienhuis, Phys. Rev. Lett. 33 (1974) 944; Phys. Rev. Lett. 35 (1975) 477; J.M.J. van Leeuwen, Phys. Rev. Lett. 34 (1975) 1056; R.H. Swendsen and S. Krinsky, Phys. Rev. Lett. 43 (1979) 177; S. Caracciolo and S. Paternello, Phys. Lett. A 126 (1988) 233;
71. [41] M. Nauenberg and B. Nienhuis, Phys. Rev. Lett. 33 (1974) 944; Phys. Rev. Lett. 35 (1975) 477; J.M.J. van Leeuwen, Phys. Rev. Lett. 34 (1975) 1056; R.H. Swendsen and S. Krinsky, Phys. Rev. Lett. 43 (1979) 177; S. Caracciolo and S. Paternello, Phys. Lett. A 126 (1988) 233;
72. [41] M. Nauenberg and B. Nienhuis, Phys. Rev. Lett. 33 (1974) 944; Phys. Rev. Lett. 35 (1975) 477; J.M.J. van Leeuwen, Phys. Rev. Lett. 34 (1975) 1056; R.H. Swendsen and S. Krinsky, Phys. Rev. Lett. 43 (1979) 177; S. Caracciolo and S. Paternello, Phys. Lett. A 126 (1988) 233;
73. [41] M. Nauenberg and B. Nienhuis, Phys. Rev. Lett. 33 (1974) 944; Phys. Rev. Lett. 35 (1975) 477; J.M.J. van Leeuwen, Phys. Rev. Lett. 34 (1975) 1056; R.H. Swendsen and S. Krinsky, Phys. Rev. Lett. 43 (1979) 177; S. Caracciolo and S. Paternello, Phys. Lett. A 126 (1988) 233;
74. [41] M. Nauenberg and B. Nienhuis, Phys. Rev. Lett. 33 (1974) 944; Phys. Rev. Lett. 35 (1975) 477; J.M.J. van Leeuwen, Phys. Rev. Lett. 34 (1975) 1056; R.H. Swendsen and S. Krinsky, Phys. Rev. Lett. 43 (1979) 177; S. Caracciolo and S. Paternello, Phys. Lett. A 126 (1988) 233;
75. [42] J. Magnen, V. Rivasseau and R. Sénéor, Phys. Lett. B 283 (1992) 90; Comm. Math. Phys. 155 (1993) 326.
76. [42] J. Magnen, V. Rivasseau and R. Sénéor, Phys. Lett. B 283 (1992) 90; Comm. Math. Phys. 155 (1993) 326.
77. [43] V.A. Alessandrini, H. J. de Vega and F. Schaposnik, Phys. Rev. B 10 (1974) 3906;
78. B 12 (1975) 5034.
79. [44] E. Langmann and G.W. Semenoff, Phys. Lett. B 297 (1992) 175; M.C. Diamantini, P. Sodano, E. Langmann and G.W. Semenoff, Nucl. Phys. B 406 (1993) 595.
80. [44] E. Langmann and G.W. Semenoff, Phys. Lett. B 297 (1992) 175; M.C. Diamantini, P. Sodano, E. Langmann and G.W. Semenoff, Nucl. Phys. B 406 (1993) 595.
81. [45] V. Branchina, H. Mohrbach and J. Polonyi, in preparation.
82. [46] I.G. Halliday and A. Schwimmer, Phys. Lett. 101B (1981) 327.
83. [47] G. Bhanot and M. Creutz, Phys. Rev. D 24 (1981) 3212; R. Dashen, U.M. Heller and H. Neuberger, Nucl. Phys. B 215 (1983) 380.
84. [47] G. Bhanot and M. Creutz, Phys. Rev. D 24 (1981) 3212; R. Dashen, U.M. Heller and H. Neuberger, Nucl. Phys. B 215 (1983) 380.
85. [48] G. Bhanot, R. Dashen, Phys. Lett. 113B (1982) 299.
86. [49] M. Bernaschi et al. Phys. Lett. B 231 (1989) 157; L.A. Fernandez et al. Phys. Lett. B 217 (1989) 314.
87. [49] M. Bernaschi et al. Phys. Lett. B 231 (1989) 157; L.A. Fernandez et al. Phys. Lett. B 217 (1989) 314.
88. [50] E. Fradkin, Field Theories of Condensed Matter Systems (Addison-Wesley, New York, 1991).
89. [51] J. Fingberg, U.M. Heller and V. Mitryushkin, Nucl. Phys. B 435 (1995) 311.
90. [52] V. Branchina and J. Polonyi, in preparation.
91. [53] Y. Shamir, The Standard Model from a New Phase Transition on the Lattice, e-Print Archive: hep-lat/9512019.