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
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.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
L. J. de Jongh and A. R. Miedema, Adv. Phys 23 (1974) 1.
R. J. Birgeneau, H. J. Guggenheim and G. Shirane, Phys. Rev. B1 (1970) 2211; B8 (1973) 304.
H. Ikeda and K. Hirakawa, J. Phys. Soc. Jpn 33 (1972) 393.
K. Hirakawa and H. Ikeda, J. Phys. Soc. Jpn. 35 (1973) 1328; 35 (1973) 1608.
L. Onsager, Phys. Rev. 65 (1944) 117; 76 (1949) 1244.
C. N. Yang, Phys. Rev 85 (1952) 808.
R. B. Griffiths, Phys. Rev. Lett 24 (1970) 1479.
M. E. Fisher, Rep. Prog. Phys 30 (1967) 615.
D. J. Breed, Physica 37 (1967) 35.
H. Ikeda and K. Hirakawa, Solid State Comm. 14 (1974) 529.
F. Samuelsen, Phys. Rev. Lett 31 (1973) 936.
N. B. Mermin and H. Wagner, Phys. Rev. Lett 17 (1966) 1133.
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.
A. A. Migdal, Zh. Eksp. Teor. Fiz. 69 (1975) 1457; Sov. Phys. JETP 42 (1976) 743.
A. M. Polyakov, Phys. Lett 59B (1975) 79.
E. Brezin and J. Zinn-Justin, Phys. Rev. Lett 36 (1976) 691.
V. L. Berezinski, Sov. Phys. JETP 32 (1971) 493; 34 (1972) 610.
V. L. Berezinski and A. Y. Blank, Sov. Phys. JETP 37 (1973) 369.
V. L. Pokrovsky and G. V. Uimin, Adv. Phys 28 (1979) 595.
H. E. Stanley and T. A. Kaplan, Phys. Rev. Lett 17 (1966) 913.
H. E. Stanley, Phys. Rev. Lett 20 (1968) 589.
J. M. Kosterlitz and D. J. Thouless, J. Phys C6 (1973) 1181.
J. M. Kosterlitz, J. Phys. CI (1974) 1047.
J. Villain, J. Physique 35 (1974) 27; 36 (1975) 581.
J. Tobochnik and G. V. Chester, Phys. Rev B20 (1979) 3761.
D. P. Landau and K. Binder, Phys. Rev B24 (1981) 1391.
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.
C. Kawabata and K. Binder, Solid State Comm. 22 (1977) 705.
M. Suzuki, S. Miyashita, A. Kuroda and C. Kawabata, Phys. Lett 60A (1977) 478.
C. Kawabata and A. R. Bishop, J. Phys. Soc. Jpn 52 (1983) 27.
B. D. Josephson, Physics Lett. 21 (1966) 608.
A. N. Berker and D. R. Nelson, Phys. Rev B19 (1979) 2388.
D. D. Betts in Phase Transition and Critical Phenomena, Domb and Green Eds., Vol. 4, Academic Press, 1974, p. 569.
H. E. Stanley, Phys. Rev. Lett 20 (1968) 589.
J. Rogiers, T. Lookmann, D. D. Betts and C. J. Elliot, Can. J. Phys 56 (1978) 409.
H. de Raedt, B. de Raedt, J. Fivez and A. Lagendijk, Physics Lett. 104 (1984) 430.
A. Lagendijk and H. de Raedt, Phys. Rev. Lett 49 (1982) 602.
H. de Raedt, B. de Raedt and A. Lagendijk, Z. Phys. B57 (1984) 209.
H. de Raedt and A. Lagendijk, Helvetica Physica Acta 56 (1983) 593.
D. D. Betts, Physica 86-88B (1977) 556.
P. Bloembergen, Physica 85B (1977) 51; H. A. Algra, L. J. de Jongh and R. L. Carlin, Physica 93B (1978) 24.
M. Steiner, J. Villain and G. Windsor, Adv. Physics 25 (1976) 87.
R. Savit, Phys. Rev B17 (1978) 1340.
R. Savit, Rev. Mod. phys 52 (1980) 453.
W. F. Vinen in Progress in Low Temperature Physics C. J. Gorter Ed., Vol. 3, North Holland Publishing Company, Amsterdam, 1955.
J. de Boer in theProceeding of the International School of Physics Enrio Fermi, Liquid Helium, G. Garezi Ed., 1967
T. C. Padmore, Phys. Rev. Lett 32 (1974) 826.
J. E. Rutledge, W. L. McMillan, J. M. Mucheland and T. E. Washburn, Phys. Rev B18 (1978) 2155.
J. R. Banavar and D. Jasnow, J. Phys. All (1978) 1361.
T. Matsubara and H. Matsuda, Prog. Theor. Phys. 16 (1956) 569; 17 (1957) 19.
B. I. Halperin and P. C. Hohenberg, Phys. Rev 188 (1969) 898.
D. R. Nelson and J. M. Kosterlitz, Phys. Rev. Lett 39 (1977) 1201.
V. L. Pokrovsky and G. V. Uimin, Physics Lett 45A (1973) 467; Sov. Phys. JETP 38 (1974) 847; Adv. Phys 28(1979)595.
D. R. Nelson and P. S. Fisher, Phys. Rev B16 (1977) 4945.
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.
I. Rudnick, Phys. Rev. Lett 40 (1978) 1454.
A. F. Hebard and A. T. Fiory, Phys. Rev. Lett 44 (1980) 291.
S. Hikami and T. Tsuneto, Prog. Theor. Phys 63 (1980) 387.
J. V. Jose, L. P. Kadanoff, S. Kirkpatrick, D. R. Nelson, Phys. Rev 16 (1977) 1217.
D. R. Nelson in Phase Transitions and Critcal Phenomena, Vol. 7, Domb and Lebowitz Eds., Academic Press, 1983.
S. Teitel and C. Jayapraskash, Phys. Rev. 1983) 598.
D. H. Lee, J. D. Joannapoulos, J. W. Negele and D. P. Landau, Phys. Rev. Lett 52 (1984) 433.
S. Miyashita and H. Shiba, J. Phys. Soc. Jpn 53 (1984) 1145; H. Kawamura and S. Miyashita, J.Phys.Soc . 53(1984)4138.
J. Villain, J. Physique 38 (1977) 385.
J. V. José, Phys. Rev B20 (1979) 2167.
S. Miyashita, J. Phys. Soc. Jpn. 52 (1983) 780; 53 (1984) 44.
S. Miyashita, Prog. Theor. Phys 69 (1983) 714.
H. Kawamura and S. Miyashita, J. Phys. Soc. Jpn 53 (1984) 9.
D. L. Huber, Phys. Lett. 76A (1980) 406; 68A (1978) 125.
D. L. Huber, Phys. Rev B26 (1982) 3758.
H. J. Mikeska, J. Phys. Cl 1 (1978) L29; C13 (1980) 2913.
J. Villain, Physica B79 (1975) 1.
K. Maki, Phys. Rev B24 (1981) 335.
G. Müller, H. Thomas, H. Beck and J. C. Bonner, Phys. Rev B24 (1981) 1429.
J. C. Bonner and G. Müller, Phys. Rev B29 (1984) 5216.
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.
J. Rogiers, E. W. Grundke and D. D. Betts, Can. J. Phys 57 (1979) 1719.
D. D. Betts and S. B. Kelland, J. Phys. Soc. Jpn 52 (1983) Suppl. 11.
M. Suzuki, Prog. Theor. Phys 56 (1976) 1454.
M. Suzuki, S. Miyashita and A. Kuroda, Prog. Theor. Phys 58 (1877) 1377.
S. Eymond and A. Durif, Mat. Res. Bull 4 (1969) 595.
S. Eymond, Thesis, University of Grenoble (1968), unpublished.
J. Y. Henry, Thesis, University of Grenoble (1976), unpublished.
G. Ladwig and B. Ziemer, Z. anorg. allg. Chem 457 (1979) 143.
L. P. Regnault, unpublished results.
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.
H. Hahn and W. Klingen, Natürwiss 52 (1968) 494.
R. Brec, G. Ouvrard, A. Louisy and J. Rouxel, J. Ann. Chem. Fr 5 (1980) 499.
L. P. Regnault, J. Rossat-Mignod, J. Y. Henry and L. J. de Jongh, J. Mag. Mag. Mat 31 — 34 1205.
L. P. Regnault, J. Rossat-Mignod, L. J. de Jongh and J. Y. Henry, to be published.
G. S. Rushbrooke and P. J. Wood, J. Mol. Phys. 1 (1958 (1958) 257; 6 (1963) 409.
L. P. Regnault, J. Rossat-Mignod and J. Y. Henry, J. Phys. Soc. Jpn 52 (1983) Suppl. 1.
L. P. Regnault, J. Y. Henry, J. Rossat-Mignod and A. de Combarieu, J. Mag. Mag. Mat 15-18 (1980) 1021.
D. W. Engelfriet, W. L. Groeneveld and G. M. Nap, Z. Naturforsch. 35a (1980) 1382.
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.
P. A. Lindgard and A. Kowalska, J. Phys C9 (1976) 2081.
E. Rastelli, A. Tassi and L. Reatto, Physica 97B (1979) 1.
L. P. Regnault, Thesis, University of Grenoble (1981), unpublished.
K. Hirakawa, H. Yoshizawa, J. D. Axe and G. Shirane, J. Phys. Soc. Jpn 52 (1983) Suppl. 19.
K. R. Atkins and I. Rudnick in Progress in Low Temperature Physics C. J. Gorter Ed., Vol. VI, Chap. 2, North Holland, Amsterdam, 1970.
L. P. Regnault, P. Burlet and J. Rossat-Mignod, Physica 86-88B (1977) 660.
L. P. Regnault, J. Rossat-Mignod, J. Villain and A. DeCombarieu, J. Physique 39 (1978) C6 - 759.
L. P. Regnault and J. Rossat-Mignod, J. Mag. Mag. Mat 14 (1979) 194.
A. Guinier, Théorie et technique de la Crystallographie, Dunod, Paris, 1956.
J. Villain, Thesis, unpublished.
L. P. Regnault, J. Rossat-Mignod, A. Adam, D. Billerey and C. Terrier, J. Physique 43 (1982) 1283.
J. Villain, personal communication.
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.
L. P. Regnault, J. Rossat-Mignod, L. J. de Jòngh and J. Y. Henry, to be published.
S. Funahashi, F. Moussa and M. Steiner, Solid State Comm. 18 (1976) 433.
S. Borovik-Romanov, N. M. Kreines, R. Laiho, T. Levóla and V. G. Zhotikov, J. Phys. C 13 (1980) 879.
H. Yamazaki, J. Phys. Soc. Jpn 37 (1974) 667.
K. Hirakawa and K. Ubukoshi, J. Phys. Soc. Jpn 50 (1981) 1909.
K. Hirakawa, H. Yoshizawa and K. Ubukoshi, J. Phys. Soc. Jpn 51 (1982) 2151.
K. Hirakawa, J. Appi Phys 53 (1982) 1893.
F. Moussa and J. Villain, J. Phys C9 (1976) 4433.
F. Moussa, B. Hennion, J. Möns and G. Peppy, Solid State Comm. 27 (1978) 141.
K. Hirakawa, H. Yoshizawa, J. D. Axe and G. Shirane, J. Phys. Soc. Jpn 52 (1983) 4220.
I. Yamada, J. Phys. Soc. Jpn 33(1972)979.
S. Flandrois, J. Masson, J. C. Rouillon, J. Gaultier and C. Hauw, Synthetic Metals 3 (1981) 1.
Yu. S. Karimov, Sov. Phys. JETP 38 (1974) 129; 39 (1974) 547; 41 (1976) 772.
Yu. S. Karimov and Yu. N. Noviko, JETP Lett. 19 (1974) 159.
M. Suzuki and H. Ikeda, J. Phys. C 14 (1981) L923.
M. Suzuki, H. Ikeda, Y. Murakami, M. Matsuura, H. Suematsu, R. Nishitani and R. Yoshizaki, J. Mag. Mag. Mat 31-34 (1983) 1173.
C. Simon, F. Batallan, I. Rosenman, J. Schweitzer, H. Lauter and R. Vangelisti, Synthetic Metals 8(1983)53.
Y. Murakami, M. Matsuura, M. Suzuki and H. Ikeda, J. Mag. Mag. Mat 31-34 (1983) 1171.
M. Suzuki, H. Ikeda and Y. Endoh, Synthetic Metals 8 (1983) 43.
C. Ayache, C. Simon, F. Batallan and I. Rosenman, to be published.
M. T. Hutchings, J. Phys. C6 (1973) 3143.
M. Elahy and G. Dresselhauss, Phys. Rev B30 (1984) 7225.
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.
M. Shayegan, L. Salamanca-Riba, J. Heremans, G. Dresselhauss and J. P. Issi ibid., p. 213.
L. J. de Jongh in Recent Developments in Condensed Matter Physics, J. T. Devreese Ed., (Plenum Publishing Corporation, 1981, Vol. 1, p. 343.
J. Villain, Proceeding of Inst. Phys. Conf. Ser. n° 64: Section 4 (1982) 239.
E. Loh, D. J. Scalapino and P. M. Grant, PHYS. Rev B31 (1985) 4712; Phys. Rev B33 (1986)5104.
F. G. Mertens, A. R. Bishop, G. M. Wysin and C. Kawabata, Phys. Rev. Lett 59 (1987) 117.
D. G. Rancourt, J. Mag. Mag. Mat 51 (1985) 133.
L. P. Regnault, J. P. Boucher, J. Rossat-Mignod, J. Bouillot, R. Pynn, J. Y. Henry and J. P. Renard, Physica 136B (1986) 329.
J. Villain, Physica 86-88B (1977)631.
L. P. Regnault and T. Chattopadhay, unpublished results.
R. Loft and T. A. DeGrand, Phys. Rev B35 (1987) 8528.
R. Coté and A. Griffin, Phys. Rev B34 (1986) 6240.
H. Zabel and S. M. Shapiro, Phys. Rev B36 (1988) 7292.
D. G. Wiesler, H. Zabel and S. M. Shapiro, Physica B156 & 157 (1989) 292.
J. Rogerie, Ch. Simon, 1. Rosenman, J. Schweitzer, Ch. Vettier, R. Vangelisti and P. Pernod, J. de Physique C8 (1988) 1437.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1990 Kluwer Academic Publishers
About this chapter
Cite this chapter
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
Download citation
DOI: https://doi.org/10.1007/978-94-009-1860-3_6
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-010-7329-5
Online ISBN: 978-94-009-1860-3
eBook Packages: Springer Book Archive