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Abstract

In the past ten years a great deal of effort in condensed matter physics has been devoted to theoretical and experimental studies of phase transitions in two- dimensional (2-d) systems (see for example the review article by De Jongh and Miedema [1]). For such systems the thermodynamic behaviour can be described by the general Hamiltonian: H

$$ = - \mathop \sum \limits_{i,j} J_{ij}^ \bot (S_i^xS_j^x + S_i^yS_j^y) + J_{ij}^\parallel S_i^zS_j^z$$
(1)

where the superscripts ⊥ and ∥ are defined relative to the z-axis (perpendicular to the XY plane) and J ij and J ij represent the (anisotropic) exchange interaction between spins i and j.

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References

  1. L. J. de Jongh and A. R. Miedema, Adv. Phys 23 (1974) 1.

    Article  ADS  Google Scholar 

  2. R. J. Birgeneau, H. J. Guggenheim and G. Shirane, Phys. Rev. B1 (1970) 2211; B8 (1973) 304.

    Google Scholar 

  3. H. Ikeda and K. Hirakawa, J. Phys. Soc. Jpn 33 (1972) 393.

    Article  ADS  Google Scholar 

  4. K. Hirakawa and H. Ikeda, J. Phys. Soc. Jpn. 35 (1973) 1328; 35 (1973) 1608.

    Google Scholar 

  5. L. Onsager, Phys. Rev. 65 (1944) 117; 76 (1949) 1244.

    Google Scholar 

  6. C. N. Yang, Phys. Rev 85 (1952) 808.

    Article  ADS  MATH  Google Scholar 

  7. R. B. Griffiths, Phys. Rev. Lett 24 (1970) 1479.

    Google Scholar 

  8. M. E. Fisher, Rep. Prog. Phys 30 (1967) 615.

    Article  ADS  Google Scholar 

  9. D. J. Breed, Physica 37 (1967) 35.

    Article  ADS  Google Scholar 

  10. H. Ikeda and K. Hirakawa, Solid State Comm. 14 (1974) 529.

    Article  ADS  Google Scholar 

  11. F. Samuelsen, Phys. Rev. Lett 31 (1973) 936.

    Article  ADS  Google Scholar 

  12. N. B. Mermin and H. Wagner, Phys. Rev. Lett 17 (1966) 1133.

    Article  ADS  Google Scholar 

  13. G. S. Rushbrooke, G. A. Baker and P. J. Wood in Phase Transition and Critical phenomena, Domb and Green Eds., Vol. 3, Academic Press 1974, p. 245.

    Google Scholar 

  14. A. A. Migdal, Zh. Eksp. Teor. Fiz. 69 (1975) 1457; Sov. Phys. JETP 42 (1976) 743.

    Google Scholar 

  15. A. M. Polyakov, Phys. Lett 59B (1975) 79.

    Google Scholar 

  16. E. Brezin and J. Zinn-Justin, Phys. Rev. Lett 36 (1976) 691.

    Article  ADS  Google Scholar 

  17. V. L. Berezinski, Sov. Phys. JETP 32 (1971) 493; 34 (1972) 610.

    Google Scholar 

  18. V. L. Berezinski and A. Y. Blank, Sov. Phys. JETP 37 (1973) 369.

    ADS  Google Scholar 

  19. V. L. Pokrovsky and G. V. Uimin, Adv. Phys 28 (1979) 595.

    Article  ADS  Google Scholar 

  20. H. E. Stanley and T. A. Kaplan, Phys. Rev. Lett 17 (1966) 913.

    Article  MathSciNet  ADS  Google Scholar 

  21. H. E. Stanley, Phys. Rev. Lett 20 (1968) 589.

    Article  ADS  Google Scholar 

  22. J. M. Kosterlitz and D. J. Thouless, J. Phys C6 (1973) 1181.

    ADS  Google Scholar 

  23. J. M. Kosterlitz, J. Phys. CI (1974) 1047.

    Google Scholar 

  24. J. Villain, J. Physique 35 (1974) 27; 36 (1975) 581.

    Google Scholar 

  25. J. Tobochnik and G. V. Chester, Phys. Rev B20 (1979) 3761.

    Article  ADS  Google Scholar 

  26. D. P. Landau and K. Binder, Phys. Rev B24 (1981) 1391.

    ADS  Google Scholar 

  27. R. W. Gerling and D. P. Landau in Magnetic Excitations and Fluctuations Lovesey Et Al. Eds., Springer series in Solid State Sciences, Vol. 54, Springer, 1984, p. 61.

    Google Scholar 

  28. C. Kawabata and K. Binder, Solid State Comm. 22 (1977) 705.

    Article  ADS  Google Scholar 

  29. M. Suzuki, S. Miyashita, A. Kuroda and C. Kawabata, Phys. Lett 60A (1977) 478.

    Article  Google Scholar 

  30. C. Kawabata and A. R. Bishop, J. Phys. Soc. Jpn 52 (1983) 27.

    Google Scholar 

  31. B. D. Josephson, Physics Lett. 21 (1966) 608.

    Article  ADS  Google Scholar 

  32. A. N. Berker and D. R. Nelson, Phys. Rev B19 (1979) 2388.

    Google Scholar 

  33. D. D. Betts in Phase Transition and Critical Phenomena, Domb and Green Eds., Vol. 4, Academic Press, 1974, p. 569.

    Google Scholar 

  34. H. E. Stanley, Phys. Rev. Lett 20 (1968) 589.

    Article  ADS  Google Scholar 

  35. J. Rogiers, T. Lookmann, D. D. Betts and C. J. Elliot, Can. J. Phys 56 (1978) 409.

    Article  ADS  Google Scholar 

  36. H. de Raedt, B. de Raedt, J. Fivez and A. Lagendijk, Physics Lett. 104 (1984) 430.

    Article  ADS  Google Scholar 

  37. A. Lagendijk and H. de Raedt, Phys. Rev. Lett 49 (1982) 602.

    Article  MathSciNet  ADS  Google Scholar 

  38. H. de Raedt, B. de Raedt and A. Lagendijk, Z. Phys. B57 (1984) 209.

    MathSciNet  Google Scholar 

  39. H. de Raedt and A. Lagendijk, Helvetica Physica Acta 56 (1983) 593.

    Google Scholar 

  40. D. D. Betts, Physica 86-88B (1977) 556.

    Google Scholar 

  41. P. Bloembergen, Physica 85B (1977) 51; H. A. Algra, L. J. de Jongh and R. L. Carlin, Physica 93B (1978) 24.

    Google Scholar 

  42. M. Steiner, J. Villain and G. Windsor, Adv. Physics 25 (1976) 87.

    Article  ADS  Google Scholar 

  43. R. Savit, Phys. Rev B17 (1978) 1340.

    Article  ADS  Google Scholar 

  44. R. Savit, Rev. Mod. phys 52 (1980) 453.

    Article  MathSciNet  ADS  Google Scholar 

  45. W. F. Vinen in Progress in Low Temperature Physics C. J. Gorter Ed., Vol. 3, North Holland Publishing Company, Amsterdam, 1955.

    Google Scholar 

  46. J. de Boer in theProceeding of the International School of Physics Enrio Fermi, Liquid Helium, G. Garezi Ed., 1967

    Google Scholar 

  47. T. C. Padmore, Phys. Rev. Lett 32 (1974) 826.

    Article  ADS  Google Scholar 

  48. J. E. Rutledge, W. L. McMillan, J. M. Mucheland and T. E. Washburn, Phys. Rev B18 (1978) 2155.

    Article  ADS  Google Scholar 

  49. J. R. Banavar and D. Jasnow, J. Phys. All (1978) 1361.

    Google Scholar 

  50. T. Matsubara and H. Matsuda, Prog. Theor. Phys. 16 (1956) 569; 17 (1957) 19.

    ADS  Google Scholar 

  51. B. I. Halperin and P. C. Hohenberg, Phys. Rev 188 (1969) 898.

    Article  ADS  Google Scholar 

  52. D. R. Nelson and J. M. Kosterlitz, Phys. Rev. Lett 39 (1977) 1201.

    Article  ADS  Google Scholar 

  53. V. L. Pokrovsky and G. V. Uimin, Physics Lett 45A (1973) 467; Sov. Phys. JETP 38 (1974) 847; Adv. Phys 28(1979)595.

    Google Scholar 

  54. D. R. Nelson and P. S. Fisher, Phys. Rev B16 (1977) 4945.

    Article  MathSciNet  ADS  Google Scholar 

  55. D. J. Bishop and J. D. Reppy, Pays. Rev. Lett. 40 (1978) 1727: B. A. Huberman, R. J. Myerson and S. Doniach, Phys. Rev. Lett. 40 (1978) 780: V. Ambegaokar, B. 1. Halperin, D. R. Nelson and E. D. Siggia, Phys. Rev. Lett 40 (1978) 783.

    Article  MathSciNet  Google Scholar 

  56. I. Rudnick, Phys. Rev. Lett 40 (1978) 1454.

    Article  ADS  Google Scholar 

  57. A. F. Hebard and A. T. Fiory, Phys. Rev. Lett 44 (1980) 291.

    Article  ADS  Google Scholar 

  58. S. Hikami and T. Tsuneto, Prog. Theor. Phys 63 (1980) 387.

    Article  ADS  Google Scholar 

  59. J. V. Jose, L. P. Kadanoff, S. Kirkpatrick, D. R. Nelson, Phys. Rev 16 (1977) 1217.

    Google Scholar 

  60. D. R. Nelson in Phase Transitions and Critcal Phenomena, Vol. 7, Domb and Lebowitz Eds., Academic Press, 1983.

    Google Scholar 

  61. S. Teitel and C. Jayapraskash, Phys. Rev. 1983) 598.

    Google Scholar 

  62. D. H. Lee, J. D. Joannapoulos, J. W. Negele and D. P. Landau, Phys. Rev. Lett 52 (1984) 433.

    Article  ADS  Google Scholar 

  63. S. Miyashita and H. Shiba, J. Phys. Soc. Jpn 53 (1984) 1145; H. Kawamura and S. Miyashita, J.Phys.Soc . 53(1984)4138.

    Google Scholar 

  64. J. Villain, J. Physique 38 (1977) 385.

    Google Scholar 

  65. J. V. José, Phys. Rev B20 (1979) 2167.

    Google Scholar 

  66. S. Miyashita, J. Phys. Soc. Jpn. 52 (1983) 780; 53 (1984) 44.

    Google Scholar 

  67. S. Miyashita, Prog. Theor. Phys 69 (1983) 714.

    Article  ADS  Google Scholar 

  68. H. Kawamura and S. Miyashita, J. Phys. Soc. Jpn 53 (1984) 9.

    Article  ADS  Google Scholar 

  69. D. L. Huber, Phys. Lett. 76A (1980) 406; 68A (1978) 125.

    Google Scholar 

  70. D. L. Huber, Phys. Rev B26 (1982) 3758.

    Article  Google Scholar 

  71. H. J. Mikeska, J. Phys. Cl 1 (1978) L29; C13 (1980) 2913.

    Google Scholar 

  72. J. Villain, Physica B79 (1975) 1.

    Article  Google Scholar 

  73. K. Maki, Phys. Rev B24 (1981) 335.

    Article  ADS  Google Scholar 

  74. G. Müller, H. Thomas, H. Beck and J. C. Bonner, Phys. Rev B24 (1981) 1429.

    Article  Google Scholar 

  75. J. C. Bonner and G. Müller, Phys. Rev B29 (1984) 5216.

    Article  ADS  Google Scholar 

  76. T. Garel and S. Doniach, J. Phys. C13 (1980) L887: D. H. Lee and G. Grinstein, Phys. Rev. Lett. 55 (1985) 541: D. H. Lee, G. Grinstein and J.Toner, Phys. Rev. Lett. 56 (1986) 2318.

    Google Scholar 

  77. J. Rogiers, E. W. Grundke and D. D. Betts, Can. J. Phys 57 (1979) 1719.

    Article  ADS  Google Scholar 

  78. D. D. Betts and S. B. Kelland, J. Phys. Soc. Jpn 52 (1983) Suppl. 11.

    Google Scholar 

  79. M. Suzuki, Prog. Theor. Phys 56 (1976) 1454.

    Article  ADS  MATH  Google Scholar 

  80. M. Suzuki, S. Miyashita and A. Kuroda, Prog. Theor. Phys 58 (1877) 1377.

    Article  ADS  Google Scholar 

  81. S. Eymond and A. Durif, Mat. Res. Bull 4 (1969) 595.

    Article  Google Scholar 

  82. S. Eymond, Thesis, University of Grenoble (1968), unpublished.

    Google Scholar 

  83. J. Y. Henry, Thesis, University of Grenoble (1976), unpublished.

    Google Scholar 

  84. G. Ladwig and B. Ziemer, Z. anorg. allg. Chem 457 (1979) 143.

    Article  Google Scholar 

  85. L. P. Regnault, unpublished results.

    Google Scholar 

  86. A. Wiedenmann, D. Delacote, J. Rossat-Mignod, R. Buder, P. Segransan, C. Berthier, G. Ouvrard and R. Brec, Proceedings of VII International Conference on Solid Compounds of Transition Elements, Grenoble, 21—25 June, 1982.

    Google Scholar 

  87. H. Hahn and W. Klingen, Natürwiss 52 (1968) 494.

    Google Scholar 

  88. R. Brec, G. Ouvrard, A. Louisy and J. Rouxel, J. Ann. Chem. Fr 5 (1980) 499.

    Google Scholar 

  89. L. P. Regnault, J. Rossat-Mignod, J. Y. Henry and L. J. de Jongh, J. Mag. Mag. Mat 31 — 34 1205.

    Google Scholar 

  90. L. P. Regnault, J. Rossat-Mignod, L. J. de Jongh and J. Y. Henry, to be published.

    Google Scholar 

  91. G. S. Rushbrooke and P. J. Wood, J. Mol. Phys. 1 (1958 (1958) 257; 6 (1963) 409.

    Article  ADS  Google Scholar 

  92. L. P. Regnault, J. Rossat-Mignod and J. Y. Henry, J. Phys. Soc. Jpn 52 (1983) Suppl. 1.

    Google Scholar 

  93. L. P. Regnault, J. Y. Henry, J. Rossat-Mignod and A. de Combarieu, J. Mag. Mag. Mat 15-18 (1980) 1021.

    Google Scholar 

  94. D. W. Engelfriet, W. L. Groeneveld and G. M. Nap, Z. Naturforsch. 35a (1980) 1382.

    Google Scholar 

  95. L. P. Regnault, J. Rossat-Mignod, J. Y. Henry, R. Pynn and D. Petitgrand in Magnetic Excitations and Fluctuations Lovesey Et Al. Eds., Springer Series in Solid State Sciences 54 p. 201.

    Google Scholar 

  96. P. A. Lindgard and A. Kowalska, J. Phys C9 (1976) 2081.

    ADS  Google Scholar 

  97. E. Rastelli, A. Tassi and L. Reatto, Physica 97B (1979) 1.

    Google Scholar 

  98. L. P. Regnault, Thesis, University of Grenoble (1981), unpublished.

    Google Scholar 

  99. K. Hirakawa, H. Yoshizawa, J. D. Axe and G. Shirane, J. Phys. Soc. Jpn 52 (1983) Suppl. 19.

    Google Scholar 

  100. K. R. Atkins and I. Rudnick in Progress in Low Temperature Physics C. J. Gorter Ed., Vol. VI, Chap. 2, North Holland, Amsterdam, 1970.

    Google Scholar 

  101. L. P. Regnault, P. Burlet and J. Rossat-Mignod, Physica 86-88B (1977) 660.

    Google Scholar 

  102. L. P. Regnault, J. Rossat-Mignod, J. Villain and A. DeCombarieu, J. Physique 39 (1978) C6 - 759.

    Google Scholar 

  103. L. P. Regnault and J. Rossat-Mignod, J. Mag. Mag. Mat 14 (1979) 194.

    Article  ADS  Google Scholar 

  104. A. Guinier, Théorie et technique de la Crystallographie, Dunod, Paris, 1956.

    Google Scholar 

  105. J. Villain, Thesis, unpublished.

    Google Scholar 

  106. L. P. Regnault, J. Rossat-Mignod, A. Adam, D. Billerey and C. Terrier, J. Physique 43 (1982) 1283.

    Article  Google Scholar 

  107. J. Villain, personal communication.

    Google Scholar 

  108. K. Maki in Physics in One Dimension Bernasconi and Schneider Eds., Springer Series in Solid State Sciences 23 1981, p. 63; Phys. Rev B24 (1981) 3991.

    Google Scholar 

  109. L. P. Regnault, J. Rossat-Mignod, L. J. de Jòngh and J. Y. Henry, to be published.

    Google Scholar 

  110. S. Funahashi, F. Moussa and M. Steiner, Solid State Comm. 18 (1976) 433.

    Article  ADS  Google Scholar 

  111. S. Borovik-Romanov, N. M. Kreines, R. Laiho, T. Levóla and V. G. Zhotikov, J. Phys. C 13 (1980) 879.

    Article  ADS  Google Scholar 

  112. H. Yamazaki, J. Phys. Soc. Jpn 37 (1974) 667.

    Article  ADS  Google Scholar 

  113. K. Hirakawa and K. Ubukoshi, J. Phys. Soc. Jpn 50 (1981) 1909.

    Article  ADS  Google Scholar 

  114. K. Hirakawa, H. Yoshizawa and K. Ubukoshi, J. Phys. Soc. Jpn 51 (1982) 2151.

    Article  ADS  Google Scholar 

  115. K. Hirakawa, J. Appi Phys 53 (1982) 1893.

    Article  ADS  Google Scholar 

  116. F. Moussa and J. Villain, J. Phys C9 (1976) 4433.

    ADS  Google Scholar 

  117. F. Moussa, B. Hennion, J. Möns and G. Peppy, Solid State Comm. 27 (1978) 141.

    Article  ADS  Google Scholar 

  118. K. Hirakawa, H. Yoshizawa, J. D. Axe and G. Shirane, J. Phys. Soc. Jpn 52 (1983) 4220.

    Article  ADS  Google Scholar 

  119. I. Yamada, J. Phys. Soc. Jpn 33(1972)979.

    Google Scholar 

  120. S. Flandrois, J. Masson, J. C. Rouillon, J. Gaultier and C. Hauw, Synthetic Metals 3 (1981) 1.

    Article  Google Scholar 

  121. Yu. S. Karimov, Sov. Phys. JETP 38 (1974) 129; 39 (1974) 547; 41 (1976) 772.

    Google Scholar 

  122. Yu. S. Karimov and Yu. N. Noviko, JETP Lett. 19 (1974) 159.

    ADS  Google Scholar 

  123. M. Suzuki and H. Ikeda, J. Phys. C 14 (1981) L923.

    Article  ADS  Google Scholar 

  124. M. Suzuki, H. Ikeda, Y. Murakami, M. Matsuura, H. Suematsu, R. Nishitani and R. Yoshizaki, J. Mag. Mag. Mat 31-34 (1983) 1173.

    Article  ADS  Google Scholar 

  125. C. Simon, F. Batallan, I. Rosenman, J. Schweitzer, H. Lauter and R. Vangelisti, Synthetic Metals 8(1983)53.

    Google Scholar 

  126. Y. Murakami, M. Matsuura, M. Suzuki and H. Ikeda, J. Mag. Mag. Mat 31-34 (1983) 1171.

    Article  ADS  Google Scholar 

  127. M. Suzuki, H. Ikeda and Y. Endoh, Synthetic Metals 8 (1983) 43.

    Article  Google Scholar 

  128. C. Ayache, C. Simon, F. Batallan and I. Rosenman, to be published.

    Google Scholar 

  129. M. T. Hutchings, J. Phys. C6 (1973) 3143.

    Google Scholar 

  130. M. Elahy and G. Dresselhauss, Phys. Rev B30 (1984) 7225.

    Article  ADS  Google Scholar 

  131. M. Elahy and G. Dresselhauss in Intercalated Graphite, M. S. Dresselhauss, G. Dresselhauss, J. E. Fisher and M. J. Moran Eds. Elsevier/North Horth Holland, New York, 1983, vol. 20. p. 207.

    Google Scholar 

  132. M. Shayegan, L. Salamanca-Riba, J. Heremans, G. Dresselhauss and J. P. Issi ibid., p. 213.

    Google Scholar 

  133. L. J. de Jongh in Recent Developments in Condensed Matter Physics, J. T. Devreese Ed., (Plenum Publishing Corporation, 1981, Vol. 1, p. 343.

    Google Scholar 

  134. J. Villain, Proceeding of Inst. Phys. Conf. Ser. n° 64: Section 4 (1982) 239.

    Google Scholar 

  135. E. Loh, D. J. Scalapino and P. M. Grant, PHYS. Rev B31 (1985) 4712; Phys. Rev B33 (1986)5104.

    Google Scholar 

  136. F. G. Mertens, A. R. Bishop, G. M. Wysin and C. Kawabata, Phys. Rev. Lett 59 (1987) 117.

    Article  ADS  Google Scholar 

  137. D. G. Rancourt, J. Mag. Mag. Mat 51 (1985) 133.

    Article  ADS  Google Scholar 

  138. L. P. Regnault, J. P. Boucher, J. Rossat-Mignod, J. Bouillot, R. Pynn, J. Y. Henry and J. P. Renard, Physica 136B (1986) 329.

    Google Scholar 

  139. J. Villain, Physica 86-88B (1977)631.

    Google Scholar 

  140. L. P. Regnault and T. Chattopadhay, unpublished results.

    Google Scholar 

  141. R. Loft and T. A. DeGrand, Phys. Rev B35 (1987) 8528.

    Article  ADS  Google Scholar 

  142. R. Coté and A. Griffin, Phys. Rev B34 (1986) 6240.

    Article  ADS  Google Scholar 

  143. H. Zabel and S. M. Shapiro, Phys. Rev B36 (1988) 7292.

    Google Scholar 

  144. D. G. Wiesler, H. Zabel and S. M. Shapiro, Physica B156 & 157 (1989) 292.

    Google Scholar 

  145. J. Rogerie, Ch. Simon, 1. Rosenman, J. Schweitzer, Ch. Vettier, R. Vangelisti and P. Pernod, J. de Physique C8 (1988) 1437.

    Google Scholar 

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Regnault, L.P., Rossat-Mignod, J. (1990). Phase Transitions in Quasi Two-Dimensional Planar Magnets. In: de Jongh, L.J. (eds) Magnetic Properties of Layered Transition Metal Compounds. Physics and Chemistry of Meterials with Low-Dimensional Structures, vol 9. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-1860-3_6

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