Phenomenological renormalization group methods

Brazilian Journal of Physics

Volumn 29, Issue 3, 1999, Pages 579-610

  Plascak, J A ^a   Figueiredo, W ^b   Grandi, B C S ^b  

^a FEDERAL UNIVERSITY OF MINAS GERAIS   (Brazil)

^b FEDERAL UNIVERSITY OF SANTA CATARINA   (Brazil)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0033242454     PISSN: 01039733     EISSN: None     Source Type: Journal    
DOI: 10.1590/s0103-97331999000300025     Document Type: Article

References (224)

1. [1] K. G. Wilson, Renormalization group and critical phenomena. I. Renormalization group and Kadanoff scaling picture, Phys. Rev. B 4, 3174 (1971); Renormalization group and critical phenomena. II. Phase-space cell analysis at critical behavior, ibidem 3184.
2. [1] K. G. Wilson, Renormalization group and critical phenomena. I. Renormalization group and Kadanoff scaling picture, Phys. Rev. B 4, 3174 (1971); Renormalization group and critical phenomena. II. Phase-space cell analysis at critical behavior, ibidem 3184.
3. [2] K. G. Wilson, The renormalization group, Rev. Mod. Phys. 773 47, (1975); see also Problems in physics with many scales of length, Sc. Am. 241, 140 (1979).
4. [2] K. G. Wilson, The renormalization group, Rev. Mod. Phys. 773 47, (1975); see also Problems in physics with many scales of length, Sc. Am. 241, 140 (1979).
5. [3] For a review, see for example, Bambi Hu, Introduction to real-space renormalization group methods in critical and chaotic problems, Phys. Rep. 91, 233 (1982).
6. [4] A.-L. Barabasi and H. E. Stanley, in Fractal Concepts in Surface Growth, Cambridge (1995).
7. [5] H. Saleur, C. G. Sammis and D. Sornette, Renormalization group of earthquakes, Nonlinear Processes Geophys. 3, 102 (1996).
8. c, Physics 2, 263 (1966).
9. [7] K. G. Wilson and M. E. Fisher, Critical exponents in 3.99 dimensions, Phys. Rev. Lett. 28, 240 (1972).
10. [8] E. Brézin, J. C. Le Guilou and J. Zinn-Justin, Field theoretical approach to critical phenomena, in Phase Transitions and Critical Phenomena, vol. 6 (London; Academic) ed C. Domb and M. S. Green (1976).
11. [9] D. J. Wallace and R. K. P. Zia, The renormalization group approach to scaling in physics, Rep. Prog. Phys. 41, 1 (1978).
12. [10] Th. Niemeijer and J. M. J. van Leeuwen, Wilson theory for spin systems on triangular lattice, Phys. Rev. Lett. 31, 1411 (1973). See also Renormalization theory for Ising-like spin systems, in Phase Transition and Critical Phenomena, vol. 6 (London, Academic) ed. C. Domb and M. S. Green (1976).
13. [10] Th. Niemeijer and J. M. J. van Leeuwen, Wilson theory for spin systems on triangular lattice, Phys. Rev. Lett. 31, 1411 (1973). See also Renormalization theory for Ising-like spin systems, in Phase Transition and Critical Phenomena, vol. 6 (London, Academic) ed. C. Domb and M. S. Green (1976).
14. [11] See, for instance, T. W. Burkhardt and J. M. J. van Leeuwen, eds., in Real Space Renormalization (Springer, Berlin, 1982).
15. [12] B. B. Mandelbrot, The Fractal Geometry of Nature, W. H. Freeman, San Francisco, (1982).
16. [13] D. Sornette, Discrete scale invariance and complex dimensions, Phys. Rep. 297, 239 (1998).
17. [14] J. M. Yeomans, in Statistical Mechanics of Phase Transition, (Oxford, Clarendon Press, 1992).
18. [15] H. J. Maris and L. P. Kadanoff, Teaching the renormalization group, Am. J. Phys. 46, 652 (1978).
19. [16] A. A. Migdal, Zh. Eksp. Fiz. 69, 810 and 1457 (1975); A. A. Migdal, Phase transitions in gauge and spin lattice systems, Sov. Phys. - JETP 42, 743 (1976); L. P. Kadanoff, Notes on Migdal's recursion formulas, Ann. Phys., NY 100, 359 (1976).
20. [16] A. A. Migdal, Zh. Eksp. Fiz. 69, 810 and 1457 (1975); A. A. Migdal, Phase transitions in gauge and spin lattice systems, Sov. Phys. - JETP 42, 743 (1976); L. P. Kadanoff, Notes on Migdal's recursion formulas, Ann. Phys., NY 100, 359 (1976).
21. [16] A. A. Migdal, Zh. Eksp. Fiz. 69, 810 and 1457 (1975); A. A. Migdal, Phase transitions in gauge and spin lattice systems, Sov. Phys. - JETP 42, 743 (1976); L. P. Kadanoff, Notes on Migdal's recursion formulas, Ann. Phys., NY 100, 359 (1976).
22. [17] R. H. Swendsen, Monte Carlo renormalization group, Phys. Rev. Lett. 42, 859 (1979); R. H. Swendsen, Monte Carlo renormalization group studies of the d = 2 Ising model, Phys. Rev. B 20, 2080 (1979).
23. [17] R. H. Swendsen, Monte Carlo renormalization group, Phys. Rev. Lett. 42, 859 (1979); R. H. Swendsen, Monte Carlo renormalization group studies of the d = 2 Ising model, Phys. Rev. B 20, 2080 (1979).
24. [18] C. Tsallis, A. M. Mariz, A. L. Stella, L. R. da Silva, Criticality of the discrete N-vector ferromagnet in planar self-dual lattices, J. Phys. A 23, 329 (1990).
25. [19] M.P. Nightingale, Scaling theory and finite systems, Physica 83A, 561 (1976).
26. [20] see R. H. Swendsen, in Real Space Renormalization T. W. Burkhardt and J. M. J. van Leeuwen, eds., (Springer, Berlin, 1982).
27. [21] C. Tsallis and A. C. N. de Magalhães, Pure and random Potts-like models: real space renormalization group approach, Phys. Rep. 268, 305 (1996).
28. [22] See, for example, J. C. Xavier, F. C. Alcaraz. D. Penã Lara and J. A. Plascak, The critical behavior of the spin-3/2 Blume-Capel model in two dimensions, Phys. Rev. B 57, 11575 (1998).
29. [23] B. Widom, Equation of state in the neighborhood of the critical point, J. Chem. Phys. 43, 3898 (1965).
30. [24] M. E. Fisher, in Proceedings of the International School Enrico Fermi, course LI, Critical Phenomena, M. S. Green, ed., Varenna, Italy (Academic Press, New York, 1971). See also M. E. Fisher and M. N. Barber, Scaling theory for finite-size effects in the critical region, Phys. Rev. Lett. 28, 1516 (1972).
31. [24] M. E. Fisher, in Proceedings of the International School Enrico Fermi, course LI, Critical Phenomena, M. S. Green, ed., Varenna, Italy (Academic Press, New York, 1971). See also M. E. Fisher and M. N. Barber, Scaling theory for finite-size effects in the critical region, Phys. Rev. Lett. 28, 1516 (1972).
32. [25] M. N. Barber, Finite size scaling, in Phase Transition and Critical Phenomena, vol. 8 (London, Academic) ed. C. Domb and J. L. Lebowitz (1983).
33. [26] R. R. dos Santos and L. Sneddon, Finite-size scaling transformations, Phys. Rev. B 23, 3541 (1981).
34. [27] J. O. Indekeu, A. Maritan and A. L. Stella, Renormalization group recursions by mean-field approximations, J. Phys. A 15, L291 (1982).
35. [28] P. M. C. de Oliveira, Finite size scaling renormalization group, Europhys. Lett. 20, 621 (1992).
36. [29] P. M. C. de Oliveira, RG based only on finite size scaling, Physica A 205, 101 (1994).
37. [30] J. M. Figueiredo Neto, S. M. Moss de Oliveira and P. M. C. de Oliveira, Finite size scaling RG: detailed description and applications to diluted Ising systems, Physica A 206, 463 (1994).
38. [31] M. P. Nightingale, Transfer matrix, phase transitions, and critical phenomena: numerical methods and applications, in Finite Size Scaling and Numerical Simulations of Statistical Systems, ed. V. Privman (World Scientific, Singapore, 1990).
39. [32] K. Croes and J. O. Indekeu, Mean-field renormalization group: Bibliography and new applications using large clusters, Mod. Phys. Lett. B (Singapore) 7, 699 (1993).
40. [33] H. A. Bethe, Statistical theory of superlattices, Proc. Roy. Soc. (London) A150, 552 (1935).
41. [34] L. Onsager, A two-dimensional model with an order-disorder transition, Phys. Rev. 65, 117 (1944).
42. [35] R. J. Baxter, Exactly Solved Models in Statistical Mechanics (Academic: London 1982).
43. [36] K. Binder, Critical behavior at surfaces, in Phase Transitions and Critical Phenomena, eds. C. Domb and J. L. Lebowitz, vol. 8, (Academic, London, 1983).
44. [37] C. Domb, Ising model, in Phase Transitions and Critical Phenomena, eds. C. Domb and M. S. Green, Vol. 3, (Academic, London, 1974).
45. [38] D. P. Landau, Computer simulation studies of critical phenomena, Physica A 205, 41 (1994).
46. [39] H. W. J. Bloete, E. Luijten and J. R. Heringa, Ising universality in three dimensions: a Monte Carlo study, J. Phys. A 28, 6289 (1995).
47. [40] A. L. Tapalov and H. W. J. Bloete, The magnetization of the 3D Ising model, J. Phys. A 29, 5727 (1996).
48. [41] J. C. Le Guillou and J. Zinn-Juntin, Critical exponents from field theory, Phys. Rev. B 21, 3976 (1980).
49. [42] D. Stauffer and A. Aharony, in Introduction to Percolation Theory (Taylor and Francis, London) second ed. (1992).
50. [43] K. De'Bell, Mean field renormalization group transformation for geometric phase transitions, J. Phys. A 16, 1279 (1983).
51. [44] K. De'Bell and T. Lookman, Mean field renormalization group calculations for directed percolation on the square lattice, J. Phys. A 17, 2733 (1984).
52. [45] S. Sarbach, Phase diagram of random spin systems: II. Bethe approximation, J. Phys. C 13, 5059 (1980).
53. [46] J. W. Essam, Percolation theory, Rep. Prog. Phys. 43, 833 (1980).
54. [47] B. K. Chakrabarti and S. S. Manna, Critical behavior of directed self-avoiding walks, J. Phys. A 16, L113 (1983).
55. [48] A. das Neves, J. Kamphorst Leal da Silva and J. A. Plascak, Some exact results from the mean field renormalization group, Physica A 189, 367 (1992).
56. [49] J. O. Indekeu, A. Maritan and A. L. Stella, Mean field renormalization group: unified approach to bulk and surface critical behavior, Phys. Rev. B 35, 305 (1987).
57. [50] P. A. Slotte, Length scaling in mean field renormalization group, J. Phys. A 20, L177 (1987).
58. [51] J. O. Indekeu and G. Menu, Corner critical exponents from the mean-field renormalization group, J. Phys. A 21, L523 (1988).
59. [52] J. H. Cardy, Critical behavior at an edge, J. Phys. A 16, 3617 (1983).
60. 2, Phys. Rev. 141, 517 (1966).
61. [54] H. W. Capel, On the possibility of first-order phase transition in Ising systems of triplet ions with zero field splitting. I. Physica 32, 966 (1966); II. ibidem 33, 295 (1967); III. ibidem 37, 423 (1967).
62. [54] H. W. Capel, On the possibility of first-order phase transition in Ising systems of triplet ions with zero field splitting. I. Physica 32, 966 (1966); II. ibidem 33, 295 (1967); III. ibidem 37, 423 (1967).
63. [54] H. W. Capel, On the possibility of first-order phase transition in Ising systems of triplet ions with zero field splitting. I. Physica 32, 966 (1966); II. ibidem 33, 295 (1967); III. ibidem 37, 423 (1967).
64. [55] M. Droz, A. Maritan and A. L. Stella, Mean field like renormalization group for disordered systems, Phys. Lett. A 92, 287 (1982).
65. [56] J. A. Plascak, Mean field renormalization group for the disordered transverse Ising model, J. Phys. A 17, L279 (1984).
66. [57] P. A. Slotte, Mean-field renormalization group transformation for the triangular Ising antiferromagnet, J. Phys. A 17, L85 (1984).
67. [58] O. F. de Alcântara Bonfim, Mean field renormalization group analysis of the Blume-Capel model, Physica A 130, 367 (1985).
68. [59] J. A. Plascak and F. C. Sá Barreto, Critical properties of the Ashkin-Teller model from the mean-field renormalization group approach, J. Phys. A 19, 2195 (1986).
69. [60] P. A. Slotte, in Phase Properties of Some Low Dimensional Models, Phd Thesis, Institutt for Teoretisk Fysikk, Norges Tekniske Høgskole, Trondheim, Norway, (1987).
70. [61] M. C. Marques, M. A. Santos and J. M. B. Oliveira, Renormalization group treatment of a random Potts model with different numbers of Potts states, J. Phys A 20, 5701 (1987).
71. [62] D. Pena Lara and J. A. Plascak, Mean field renormalization group for Ising models with S ≥ 1, Mod. Phys. Lett. B, 10 1067 (1996).
72. [63] J. Ashkin and E. Teller, Statistics of two-dimensional lattices with four components, Phys. Rev. 64, 178 (1943).
73. [64] P. M. C. Oliveira and F. C. Sá Barreto, RG studies of the Ashkin-Teller model, J. Stat. Phys. 57, 53 (1989).
74. [65] J. A. Plascak, Renormalization group study of the two-dimensional Ising model with crossing bonds, Physica A 183, 563 (1992).
75. [66] C. N. Likos and A. Maritan, Multi-interaction mean-field renormalization group, Phys. Rev. E 53, 3303 (1996).
76. [67] H. F. Verona de Resende, F. C. Sa Barreto and J. A. Plascak, Renormalization group treatment of the mixed-spin system in d-dimensional lattices, Physica A 149, 606 (1988).
77. [68] C. N. Likos, Anisotropie triangular Ising model in the extended mean-field renormalization group approach, Phys. Rev. E 55, 2001 (1997).
78. [69] J. O. Indekeu, A. L. Stella and L. Zhang, Dynamical renormalization through classical equations of motion, J. Phys. A 17, L341 (1984).
79. [70] R. J. Glauber, Time dependent statistics of the Ising model, J. Math. Phys. 4, 294 (1963).
80. [71] J. A. Plascak, Quantum spin systems: dynamical mean field renormalization group approach, J. Phys. A 17, L697 (1984).
81. [72] S. K. Ma, in Modern Theory of Critical Phenomena, (New York, W. A. Benjamin, 1976).
82. [73] N. Jan and D. Stauffer, Determination of the non-linear relaxation exponent: a Monte Carlo study, Phys. Letts. A 93, 39 (1982).
83. [74] C. de Dominicis, E. Brezin and J. Zinn-Justin, Field theoretical techniques and critical dynamics: I. Ginzburg-Landau stochastic models without energy conservation, Phys. Rev. B 12, 4945 (1975).
84. [75] J. A. Plascak, Mean field renormalization group approach for the spin-1/2 anisotropic Heisenberg model, J. Phys. A 17, L597 (1984).
85. [76] J. A. Plascak and N. P. Suva, Mean field renormalization group study of the anisotropic Ising model, J. Phys. C 19, 4493 (1986).
86. [77] Z. P. Shi and R. B. Tao, Double-chain mean-field renormalization group approach for the Ising model, Comm. Theor. Phys. (China) 12, 333 (1989).
87. [78] A. Pelizzola and A. Stella, Mean field renormalization group for the boundary magnetization of strip clusters, J. Phys. A 26, 6747 (1993).
88. [79] O. F. de Alcântara Bonfim, F. C. Sa Barreto and M. A. Moura, Two-step renormalization group for Ising systems, J. Phys. C 17, L599 (1984).
89. [80] K. F. Tang and J. Z. Hu, Exact decimation transformation with mean-field approximations, J. Phys. A 19, L621 (1986).
90. [81] M. Droz, A. Maritan and A. L. Stella, Mean field renormalization group with reaction field for diluted Ising model, Nuovo Cimento D 9, 123 (1987).
91. [82] G. Kamieniarz and R. Dekeyser, Symmetry dependent effective field, Second International School of Theoretical Physics: Symmetry and Structural Properties of Condensed Matter, 181 (1993).
92. [83] M. C. Marques and M. A. Santos, Mean field renormalization group study of surface effects in the Ising ferromagnet, Phys. Lett. A 118, 41 (1986).
93. [84] M. A. Santos, M. C. Marques and J. M. B. Oliveira, The semi-infinite Ising model with mixed ferromagnetic and antiferromagnetic interactions: a MFRG approach, J. Phys. C 21, 747 (1988).
94. [85] Q. Jiang and Z. Y. Li, Critical behavior in a semi-infinite Ising ferromagnet with random field or amorphization at the surface, J. Magn. Magn. Mat. 80, 178 (1989).
95. [86] Q. Jiang and Z. Y. Li, Study of surface magnetism in a semi-infinite Ising ferromagnetic system, Acta Phys. Sin. (China) 38, 1062 (1989).
96. [87] S. L. Xu and Z. Y. Li, Surface phase transition and tricritical point of a semi-infinite Ising ferromagnet with a surface trimodal random field. J. Magn. Magn. Mat. 87, 279 (1990).
97. [88] A. F. S. Moreira and W. Figueiredo, Ising model on a semi-infinite lattice: mean field renormalization group approach, Phys. Lett. A 163, 159 (1992).
98. [89] V. Ilkovic̃, Mean-field renormalization-group study of a semi-infinite Ising model with a spin-one free surface, Phys. Stat. Sol. B172, K19 (1992).
99. [90] Z. Y. Li, S. L. Xu, D. L. Lin and T. F. George, Surface phase diagrams of the spin-1 Ising model with a random surface field, Physica B 182, 249 (1992).
100. [91] Gang Sun and Jie Yang, Numerical calculations for the surface on a semi-infinite Ising model with a random surface field, Comm. Theor. Phys. 23, 25 (1995).
101. [92] Gang Sun, Mean-field renormalization group approaches to the surface on a semi-infinite Ising model with a random surface field, Phys. Rev. B 51, 3637 (1995).
102. [93] A. S. de Arruda and W. Figueiredo, Phase diagram of the semi-infinite Ising model in a random field, Mod. Phys. Lett. B 11, 973 (1997).
103. [94] J. A. Plascak and W. Figueiredo, Renormalization group study of compressible Ising systems, Phys. Lett. A 123, 135 (1987).
104. [95] J. A. Plascak, Ferromagnetic critical line of the Ising model with crossing bonds, Phys. Lett. A 154, 197 (1991).
105. [96] L. R. Evangelista and V. K. Saxena, Two-step renormalization group for randomly diluted Ising models, J. Phys. A 18, L389 (1985).
106. [97] L. R. Evangelista and V. K. Saxena, Critical properties of bond-and site-diluted triangular Ising model, Phys. Stat. Sol. B 137, K31 (1986).
107. [98] C. Z. Yang and Z. Y. Li, Mean field renormalization group for site-bond diluted Ising ferromagnets, Phys. Stat. Sol. B 146, 223 (1988).
108. [99] N. Benayad, A. Benyoussef and N. Boccara, Reentrant ferromagnetism in a two-dimensional Ising model with random nearest-neighbor interactions, J. Appl. Phys. 63 4001 (1988); N. Benayad, A. Benyoussef and N. Boccara, Reentrant ferromagnetism in a two-dimensional Ising model with random nearest-neighbor interactions, J. Phys. C 21, 5417 (1988).
109. [99] N. Benayad, A. Benyoussef and N. Boccara, Reentrant ferromagnetism in a two-dimensional Ising model with random nearest-neighbor interactions, J. Appl. Phys. 63 4001 (1988); N. Benayad, A. Benyoussef and N. Boccara, Reentrant ferromagnetism in a two-dimensional Ising model with random nearest-neighbor interactions, J. Phys. C 21, 5417 (1988).
110. [100] A. Rosales Rivera, G. A. Perez Alcazar, and J. A. Plascak, Diluted and random-bond Ising model: application to the Fe - Mn - Al alloys, Phys. Rev. B 41, 4774 (1990).
111. [101] J. A. Plascak and J. Kamphorst Leal da Silva, Renormalization group study of the two-dimensional site-diluted Ising model, Phys. Lett. A 159, 295 (1991).
112. [102] D. F. de Albuquerque and J. R. de Souza, Universality in the site-bond-correlated (SBC) Ising model, Phys. Lett. A 171, 421 (1992).
113. [103] E. Mina, A. Bohorgues, L. E. Zamora and G. A. Perez Alcazar, Diluted and random-bond Ising model for the Fe-Al disordered alloys, Phys. Rev. B 47, 7925 (1993).
114. [104] J. Ricardo de Souza and D. F. Albuquerque, Mean-field renormalization group: approach to diluted site-bond-correlated Ising model, Phys. Rev. B 48, 16484 (1993).
115. x system, Phys. Rev B 49, 16035 (1994).
116. [106] Ligia E. Zamora, G. A. Perez Alcazar, A. Bohorgues, A. Rosales Rivera and J. A. Plascak, Phase diagram of the diluted and random-bond Ising model, Phys. Rev. B 51, 9329 (1995).
117. [107] J. Ricardo de Souza, D. F. Albuquerque and I. P. Fittipaldi, Spin-glass phase for the diluted site-bond-correlated version, J. Magn. Magn. Mat. 149, 269 (1995).
118. 0.30 alloys series, J. Appl. Phys. 82, 6165 (1997).
119. 3, J. Appl. Phys. 81, 5297 (1997).
120. [110] E.E. Reinehr e W. Figueiredo, Phase diagram of the dilute antiferromagnetic Ising model, Phys. Letts. A 244, 165 (1998).
121. [111] A. S. de Arruda, W. Figueiredo, R. M. Sebastianes and V. K. Saxena, Field distribution and tricritical points in a random-field Ising model: Mean field renormalization group approach, Phys. Rev. B 39, 4409 (1989).
122. [112] A. das Neves and J. Kamphorst Leal da Silva, Two-dimensional site directed percolation to bulk and surface critical properties, J. Phys. A 24, 5363 (1991).
123. [113] G. Odor and A. Szolnoki, Directed-percolation conjecture for cellular automata, Phys. Rev. E 53, 2231 (1996).
124. [114] A. Surda, A renormalization group method for lattice gas models, J. Phys. A 17, 2697 (1984).
125. [115] H. Leitão and M. M. Telo da Gama, A model for two dimensional orientational order. Nematic ordered states at low temperatures, Physica A 180, 263 (1992).
126. [116] H. Leitao and M. M. Telo da Gama, in Phase Transitions in Liquid Crystals, ed. S. Martelluci and A. N. Chester (Plenum, New York, 1992).
127. [117] P. Pawlicki, G. Musial, G. Kamieniarz and J. Rogiers, Mean-field renormalization group study of a modified Ashkin-Teller model, Physica A 242, 281 (1997).
128. [118] L. de Cesare, I. Rawbuffo and D. I. Uzunov, Fluctuation effects in a class of systems with two order parameters, Mod. Phys. Lett. B 7, 1725 (1993).
129. [119] E. C. Valadares and J. A. Plascak, Mean-field renormalization group approach for the axial next-nearest-neighbor Ising model, J. Phys. A 20, 4967 (1987).
130. [120] L. S̃amaj, A theory of higher order correlations: application to mixed spin systems, Physica A 161, 432 (1989).
131. [121] M. C. Marques and M. A. Santos, Mean field renormalization group for the Potts model in a transverse field, J. Phys. C 19, 4213 (1986).
132. [122] M. A. Santos and M. C. Marques, Mean field renormalization group study of the semi-infinite Potts model, J. Phys. A 20, 6143 (1987).
133. [123] M. C. Marques and C. A. S. Santos, Tricritical point in a random Potts model, J. Phys. A 20, 5417 (1987).
134. [124] M. C. Marques, M. A. Santos and J. M. B. Oliveira, Renormalization group treatment of a random Potts model with different numbers of Potts spin states, J. Phys. A 20, 5701 (1987).
135. [125] Q. Ye, K. F. Tang and J. Z. Hu, Application of an exact decimation transformation with mean field approximation to the Potts model, Chin. Phys. 8, 630 (1988).
136. [126] M. C. Marques, Three-state Potts model with antiferromagnetic interactions: A MFRG approach, J. Phys. A 21, 1061 (1988).
137. [127] M. C. Marques, Mean field renormalization group study of the antiferromagnetic q-state Potts models, J. Phys. A 21, 1297 (1988).
138. 4 spin model, J. Phys. A 17, 2885 (1984).
139. [129] E. Niebur and J. Sólyom, Mean field like variational and renormalization group studies of (1+1)-dimensional spin models, J. Phys. A 20, 2949 (1987).
140. [130] E. Niebur and J. Sólyom, Improved mean field like renormalization group approach for Z(q) symmetric spin models, J. Phys. A 21, 539 (1988).
141. [131] M. L. Lyra and S. Coutinho, Phase diagrams for random-bond D-vector models, Physica A 155, 232 (1989).
142. [132] M. A. Continentino and S. Coutinho, The planar random anisotropic model: a mean-field renormalization group approach, J. Magn. Magn. Mat. 125, 49 (1993).
143. [133] S. T. Chen, Mean-field renormalization group for the g-state clock spin-glass model, Physica A 229, 181 (1996).
144. [134] V. Ilkovic̃, Mean field renormalization group study of the Blume-Capel model, Phys. Stat. Sol. B 166, K99 (1991).
145. [135] W. Figueiredo, Phase diagram of a spin-1 Ising model with random crystal field, Braz. J. Phys. 22, 313 (1992).
146. [136] D. Peña Lara and J. A. Plascak, Multicritical points from mean field renormalization group approach, Int. J. Mod. Phys. B 12, 1831 (1998).
147. [137] C. A. S. Santos and M. C. Marques, MFRG study of spin-1 Ising models: effects of a transverse field and randomness in the crystal-field coupling, Port. Phys. (Portugal) 18, 113 (1987).
148. [138] O. F. de Alcântara Bonfim and F. C. Sa Barreto, Renormalization group treatment of a spin-one Ising model with biquadratic exchange interaction, Phys. Lett. A 109, 341 (1985).
149. [139] Y. Gũnduç, A mean field renormalization group study of the finite temperature SU(2) lattice gauge theory at the strong coupling limit, Phys. Lett. B 208, 115 (1988).
150. [140] J. Ricardo de Souza and D. F. de Albuquerque, Critical properties of the XY and classical Heisenberg models: a renormalization group study, Physica A 236, 419 (1997).
151. [141] D. J. Bukman and J. M. J. van Leeuwen, Mean field renormalization group for the spin-1/2 XXZ model, J. Phys. A 25, 4285 (1992).
152. [142] J. Ricardo de Souza, New renormalization group approach for the spin-1/2 anisotropic Heisenberg model, Phys. Lett. A 216, 321 (1996).
153. [143] J. Ricardo de Souza and J. A. Plascak, Phase transition in the three-dimensional anisotropic Heisenberg antiferromagnetic model, Phys. Lett. A 237, 66 (1997).
154. [144] J. Ricardo de Souza, Universality in the critical exponents δ and η, Phys. Lett. A 252, 137 (1999).
155. [145] Hai-Xia Cao, Qing Jiang, Chen Xu and Zhen-Ya Li, Critical behavior of the spin-1/2 anisotropic Heisenberg ferromagnet with a transverse field, Sol. Stat. Comm. 103, 223 (1997).
156. [146] E. C. Valadares and J. A. Plascak, Diluted transverse Ising model within the mean field renormalization group approach, Phys. Lett. A 114, 95 (1986).
157. [147] C. Z. Yang and W. J. Song, Mean field renormalization group and path-integral methods for the disordered transverse Ising model, Phys. Stat. Sol. B 162, K113 (1990).
158. [148] W. J. Song and C. Z. Yang, MFRG and DPIR for a S=3/2 transverse Ising model in a random field, Phys. Stat. Sol. 183, 259 (1994).
159. [149] W. J. Song and C. Z. Yang, Study of the critical behavior for the S=5/2 transverse Ising model in a random field, Phys. Stat. Sol. 185, 227 (1994).
160. [150] W. J. Song and C. Z. Yang, The critical properties of the spin-3/2 Ising model with a transverse field, Sol. Stat. Comm. 91, 145 (1994).
161. [151] W. J. Song and C. Z. Yang, MFRG-DPIR study of spin-5/2 Ising model with a random transverse field, Sol. Stat. Comm. 92, 361 (1994).
162. [152] Z. P. Shi and R. B. Tao, Magnetic phase transitions in quantum Ising model with annealed antiferromagnetic bond randomness, Comm. Theor. Phys. (China) 13, 433 (1990).
163. [153] T. F. Cassol, W. Figueiredo and J. A. Plascak, Ising model in a random transverse field, Phys. Lett. A 160, 518 (1991).
164. [154] W. J. Song, MFRG with DPIR for the disordered Ising model in a random transverse field, Sol. Stat. Comm. 89, 379 (1994).
165. [155] W. J. Song and C. Z. Yang, MFRG-DPIR study of the Ising model. Spin-3/2 with random and spin-5/2 with fixed transverse field, Phys. Stat. Sol. 186, 511 (1994).
166. [156] L. A. Serkov and V. O. Shvalev, Ising model in a random transverse field, Phys. Sol. Stat. 36, 1847 (1994).
167. [157] W. J. Song, MFRG-DPIR study on the arbitrary spin Ising model with random transverse field, Phys. Stat. Sol. 196, 243 (1996).
168. [158] M. Droz and A. Pekalski, Mean field like renormalization group study of random two-component magnetic systems, Phys. Lett. A 107, 89 (1985).
169. [159] M. L. Martins, J. A. Plascak and F. C. Sá Barreto, Mean field renormalization group for the spin-1/2 random anisotropic Heisenberg model, Phys. Lett. A 126, 353 (1988).
170. [160] J. Sólyom, Variational approach to the spin-1 anisotropic Heisenberg chain, Phys. Rev. B 32, 7524 (1985).
171. [161] C. Z. Yang and W. J. Song, Mean field renormalization group and path-integral methods for spin-one disordered Ising model in a transverse field, Phys. Stat. Sol. B 166, 269 (1991).
172. [162] E. Granato and M. A. Continentino, Charging effects and quantum crossover in granular superconductors, Phys. Rev. B 48, 15977 (1993).
173. [163] L. A. Serkov and V. O. Shvalev, Heisenberg ferromagnet with random Dzyaloshinskii interaction: mean field renormalization group method, Phys. Sol. Stat. 36, 98 (1994).
174. [164] J. Ricardo de Souza, Study of the mean field renormalization group method with the Tsallis statistics, Physica A 235, 534 (1997).
175. [165] M. C. Marques, Critical behavior of the non-equilibrium Ising model with locally competing temperatures, J. Phys. A 22, 4493 (1989).
176. [166] T. Tome, M. J. de Oliveira and M. A. Santos, Non-equilibrium Ising model with competing Glauber dynamics: a MFRG approach, J. Phys. A 24, 3677 (1991).
177. [167] M. C. Marques, Non-equilibrium Ising model with competing dynamics: a MFRG approach, Phys. Lett. A 145, 379 (1990).
178. [168] M. C. Marques, Critical behavior of non-equilibrium three-state systems, J. of Phys. A 26, 1559 (1993).
179. [169] M. C. Marques, Application of the mean field renormalization group approach to non-equilibrium critical phenomena, Physica A 163, 915 (1990).
180. [170] M. C. Marques, Effects of dilution on the phase diagram of some non-equilibrium systems, J. Phys. A 23 ,3389 (1990).
181. [171] M. Droz, L. Frachebourg and M. C. Marques, Critical phenomena at surfaces in a model of non-equilibrium phase transitions, J. Phys. A 24, 2869 (1991).
182. [172] J. F. F. Mendes, R. Dickman, M. Henkel and M. C. Marques, Generalized scaling for models with multiple absorbing states, J. Phys. A 27, 3019 (1994).
183. [173] D. P. Landau and K. Binder, Critical behavior of the surface layer magnetism at the extraordinary transition in the three-dimensional Ising model, Phys. Rev. B 41, 4786 (1990).
184. [174] K. Binder and P. C. Hohenberg, Surface effects on magnetic phase transitions, Phys. Rev. B 9, 2194 (1974).
185. [175] Z. Y. Li and C. Z. Yang, Effective field renormalization group study for the diluted Ising model, Phys. Rev. B 37, 5744 (1988).
186. [176] N. Benayad, A. Benyoussef, N. Boccara and A. E. Kenz, Renormalization group recursion relations using the application of generalized Gallen indentities to the Ashkin-Teller model, J. Phys. C 21, 5747 (1988).
187. [177] I. P. Fittipaldi, Effective field renormalization group approach for Ising lattice spin systems, J. Magn. Magn. Mat. 131, 43 (1994).
188. [178] H. B. Callen, A note on Green functions and the Ising model, Phys. Lett. 4, 161 (1963).
189. [179] M. Suzuki, Generalized exact formulation for the correlations of the Ising model and other classical systems, Phys. Lett. 19, 267 (1965).
190. [180] R. Honmura and T. Kaneyoshi, Contributions to a new type of effective field theory of the Ising model, J. Phys. C 12, 3979 (1979).
191. [181] F. C. Sa Barreto and I. P. Fittipaldi, A simple derivation of the thermodynamic properties of the one-dimensional Ising model, Rev. Bras. Fis. (Brazil) 11, 745 (1981).
192. [182] A. Bobak and M. Jascur, A new type of effective field theory for Ising models with spin-1/2, Phys. Stat. Sol. (b) 135, K9 (1986).
193. [183] V. Ilkovic, Mean field renormalization group study for the Ising model, Phys. Stat. Sol. B 166, K31 (1991).
194. [184] L. A. Serkov, Fixed scale transformation with allowance for short-range spin correlations, Theor. Math. Phys. 92, 759 (1992).
195. [185] D. F. de Albuquerque and I. P. Fittipaldi, A unified effective field renormalization group framework approach for the quenched diluted Ising models, J. Appl. Phys. 75, 5832 (1994).
196. [186] D. F. de Albuquerque and I. P. Fittipaldi, Effective-field renormalization group (ERFG): phase diagrams of quenched bond-mixed spin Ising model on square and Kagome lattices, J. Mag. Mag. Mat. 104-107, 236 (1992).
197. [187] V. Ilkovic, Effective-field renormalization-group approach study of surface effects in the Ising Ferromagnet, Phys. Stat. Sol. B 166, K35 (1991).
198. [188] J. Ricardo de Souza, Equivalence of the O(n) vector ferromagnetic and antiferromagnetic models, Physica A 256, 383 (1998).
199. [189] Q. Jiang and Z. Y. Li, Effective field renormalization group study for the transverse Ising model in a quantum system, Phys. Rev. B 40, 11264 (1989).
200. [190] Jiang Xuefan and Zhong Jialin, The first fluctuation correction for the transverse Ising model, Phys. Stat. Sol. B 193, K5 (1996).
201. [191] J. Ricardo de Souza, Critical behavior of the quantum spin-1/2 anisotropic Heisenberg model, Physica A 259, 138 (1998).
202. [192] Ijaní G. Araújo, J. Cabral Neto and J. Ricardo de Souza, Effective field renormalization group approach for the spin-1/2 anisotropic Heisenberg antiferromagnetic model, Physica A, in press (1999).
203. [193] See D. Ruelle, in Statistical Mechanics, (Reading, W. A. Benjamin, 1976).
204. [194] R.R. Netz and A. N. Berker, Monte Carlo mean field theory and frustrated systems in two and three-dimensions, Phys. Rev. Lett. 66, 2901 (1991); Netz and Berker reply, ibidem 67, 1808 (1991).
205. [194] R.R. Netz and A. N. Berker, Monte Carlo mean field theory and frustrated systems in two and three-dimensions, Phys. Rev. Lett. 66, 2901 (1991); Netz and Berker reply, ibidem 67, 1808 (1991).
206. [195] R.R. Netz and A. N. Berker, Hard-spin mean field theory: formulation for Ising, XY and other models, J. of Appl. Phys. 70, 6074 (1991).
207. [196] E. F. Henriques and S. R. Salinas, Monte Carlo mean field method for spin systems, Phys. Rev. B 51, 8621 (1995).
208. [197] P. M. C. de Oliveira, Broad histogram method and zero dimensional quantities, to appear in Comp. Phys. Comm. (1999).
209. [198] S. Moss de Oliveira, P. M. C. de Oliveira and F. C. Sá Barreto, The spin S Blume-Capel model flow diagram, J. Stat. Phys. 78, 1619 (1995).
210. [199] P. M. C. de Oliveira, S. Moss de Oliveira, C. E. Cordeiro and D. Stauffer, Finite size scaling for first-order transitions: Potts model, J. Stat. Phys. 80, 1433 (1995).
211. [200] M. Silvério Soares, J. Kamphorst Leal da Silva and F. C. Sá Barreto, Numerical methods to evaluate the dynamical critical exponent, Phys. Rev. B 55, 1021 (1997).
212. [201] M. Silvério Soares, in Study of the spin critical dynamics through finite size scaling, PhD thesis (in portuguese) Universidade Federal de Minas Gerais, Departamento de Física, unpublished (1997).
213. [202] J. A. Plascak and J. Kamphorst Leal da Silva, On the equivalence of finite size scaling renormalization gioup and phenomenological renormalization, Physica A 233, 551 (1996).
214. [203] C. Domb, Cooperative phenomena in crystals, Ad. Phys. 9, 149 (1969).
215. [204] L. de Matos Castro and J. A. Plascak, The Blume-Capel model from finite size scaling RG with infinite strips, to be published.
216. [205] J. Kamphorst Leal da Silva, R. Alves Nogueira, J. A. Plascak and M. Droz, A new mean field renormalization group transformation, J. Phys. A 27, 1495 (1994).
217. [206] M. Suzuki, Statistical mechanical theory of cooperative phenomena. I. General theory of fluctuations, coherent anomalies and scaling exponents with simple applications to critical phenomena, J. Phys. Soc. Japan 55. 4205 (1986).
218. [207] M. Suzuki, M. Katori and X. Hu, Coherent anomaly method in critical phenomena. I., J. Phys. Soc. Japan 56, 3092 (1987).
219. [208] F. O. Coelho and J. A. Plascak, The new mean field renormalization group from effective field theory, Mod. Phys. Lett. B 9, 1617 (1995).
220. [209] S. R. White, Density matrix formulation for quantum renormalization groups, Phys. Rev. Lett. 69, 2863 (1992).
221. [210] S. R. White, Density matrix algorithms for quantum renormalization groups, Phys. Rev. B 48, 10345 (1993).
222. [211] R. M. Noack, S. R. White and D. J. Scalapino, Correlations in a two-chain Hubbard model, Phys. Rev. Lett. 73, 882 (1994).
223. [212] Tomotoshi Nishino, Density matrix renormalization group method for 2D classical models, J. Phys. Soc. Jp. 64, 3598 (1995).
224. [213] S. R. White, Strongly correlated electrons systems and the density matrix renormalization group, Phys. Rep. 301, 187 (1998).