Phase transitions in spin systems with frustrations

References

• Adam , A. , Billerey , D. , Terrier , C. , Mainard , R. , Regnault , L. P. , Rossat-Mignod , J. and Meriel , P. 1980 . Neutron diffraction study of the commensurate and incommensurate magnetic structure of NiBr2 . Sol. State Commun. , 35 : 1
   Google Scholar
• Aharony , A. 1975 . Critical behaviour of amorphous magnets . Phys. Rev. , B12 : 1038
   Google Scholar
• Aharony , A. , Domany , E. , Hornreich , R. M. , Schneider , T. and Zannetti , M. 1985 . Novel Lifshitz tricritical point and critical dynamics . Phys. Rev. , B32 : 3358
   Google Scholar
• Anderson , P. W. 1973 . Resonating valence bonds: a new kind of insulator? . Mater. Res. Bull. , 8 : 153
   Web of Science ®Google Scholar
• Andre , G. , Bidaux , R. , Carton , J. P. , Conte , R. and de Sere , L. 1979 . Frustration in periodic systems: exact results for some 2D Ising models . J. Physique , 40 : 479
   Google Scholar
• Aplesnin , S. S. 1980 . Phase diagrams of disordered magnets and their behaviour at low temperatures. Magnetic and resonant properties of magnetic materials . Krasnoyarsk , : 41 – 70 .
   Google Scholar
• Belobrov , P. I. , Gekht , R. S. and Ignatchenko , V. A. 1983 . Ground state in systems with dipole interaction. . Zh. Eksp. Teor. Fiz. , 84 : 1097
   Google Scholar
• 1983 . Sov. Phys. JETP , 57 : 636
   Google Scholar
• Berezinsky , V. L. 1970 . Destruction of long-range order in 1D and 2D systems with continuous symmetry group. Classical systems . Zh. Eksp. Teor. Fiz. , 59 : 907
   Google Scholar
• Birgeneau , R. J. , Shirane , G. and Kitchens , T. A. Proceedings of the 14th Low Temperature Conference . 1975 , Colorado.
   Google Scholar
• Blankschtein , D. , Ma , M. , Berker , A. N. , Crest , G. S. and Soukoulis , C. M. 1984 . Ordering of a stacked frustrated triangular system in three dimensions . Phys. Rev. , B29 : 5256
   Google Scholar
• Borouch , E. and McCoy , B. M. 1971 . Statistical mechanics of the XY model . Phys. Rev. , A3 : 786
   Google Scholar
• Choi , M. Y. and Stroud , D. 1985 . Critical behaviour of pure and diluted XY models with uniform frustrations . Phys. Rev. , B32 : 5773
   Google Scholar
• De Fotis , C. C. 1981 . Magnetism of solid oxygen . Phys. Rev. , B23 : 4714
   Google Scholar
• Dotsenko , Vik , S. and Dotsenko , S. VI. 1983 . Critical behaviour of the phase transition in the 2D Ising model with impurities . Adv. Phys. , 32 : 129
   Web of Science ®Google Scholar
• Dotsenko , Vik , S. and Dotsenko , S. VI. 1984 . Critical behaviour of the Baxter model with impurity lattice bonds . J. Phys. , A17 : L301
   Google Scholar
• Fazekas , P. and Anderson , P. W. 1974 . On the ground state properties of the anisotropic triangular antiferromagnet . Philos. Mag. , 30 : 423
   Web of Science ®Google Scholar
• Fedoseeva , N. V. , Gekht , R. S. , Velikanova , T. A. and Balaev , A. D. 1985 . New intermediate phase in spiral antiferromagnet CsCuCl3 induced by high magnetic field. . Pis'ma Zh. Eksp. Teor. Fiz. , 41 : 332
   Google Scholar
• 1985 . JETP Lett. , 41 : 406
   Google Scholar
• Ferdinand , A. E. and Fisher , M. E. 1969 . Bounded and inhomogeneous Ising models. I. Specific heat anomaly of a finite lattice . Phys. Rev. , 185 : 832
   Web of Science ®Google Scholar
• Forgacs , G. 1980 . Ground-state correlations and universality in two-dimensional fully frustrated systems . Phys. Rev. , B22 : 4473
   Google Scholar
• Gaulin , B. D. , Collins , M. F. and Buyers , W. J. L. 1987 . Spin waves in the triangular antiferromagnet CsMnBr3 . J. Appl. Phys. , 61 : 3409
   Google Scholar
• Geilikman , M. B. 1974 . Spontaneous magnetization and correlation functions in Kagome lattice . Zh. Eksp. Teor. Fiz. , 66 : 1166
   Google Scholar
• Gekht , R. S. 1984 . Incommensurate structures with vortical configurations in dipole systems. . Zh. Eksp. Teor. Fiz. , 87 : 2095
   Google Scholar
• 1984 . Sov. Phys. JETP , 60 : 1210
   Google Scholar
• Gekht , R. S. 1985 . Sinusoidal incommensurate structure in spiral antiferromagnets . Sol. State Commun. , 55 : 709
   Google Scholar
• Gekht , R. S. 1986 . Collective modes of incommensurate structures in systems with dipole interactions. . Zh. Eksp. Teor. Phys. , 91 : 190
   Google Scholar
• 1986 . Sov. Phys. JETP , 64 : 110
   Google Scholar
• Gekht , R. S. 1987 . Magnetic transition from an incommensurate into commensurate intermediate one, and low-temperature spin correlations. . Zh. Eksp. Teor. Fiz. , 93 : 255
   Google Scholar
• 1987 . Sov. Phys. JETP , 66 : 147
   Google Scholar
• Gekht , R. S. and Ignatchenko , V. A. 1981 . Magnetic states in structures with a spatially periodic distribution of ferromagnetic particles. . Fiz. Nizk. Temp. , 7 : 1176
   Google Scholar
• 1981 . Sov. J. Low Temp. Phys. , 7 : 571
   Google Scholar
• Glazman , L. I. and Tsukernik , V. M. 1980 . Exact solution of complex two-diemnsional Ising lattice . Pis'ma Zh. Eksp. Teor. Fiz. , 81 : 410
   Google Scholar
• Harris , A. B. 1974 . Effect of random defects on the critical behaviour of Ising models . J. Phys. , C7 : 1671
   Google Scholar
• Haseda , T. , Wada , N. , Hata , M. and Amaya , K. 1981 . Spin ordering in a triangular XY antiferromagnetic: CsFeCl3 and RbFeCl3 . Physica , B108 : 841
   Google Scholar
• Hirakawa , K. , Ikeda , H. , Kadowaki , H. and Ubukoshi , K. 1983 . Magnetic susceptibilities of the frustrated triangular lattice antiferromagnets CsVCl3 and VX2 (X = Cl, Br, I): appearance of magnetic liquid in the ordered state . J. Phys. Soc. Japan , 52 : 2882
   Google Scholar
• Hoever , P. and Zittartz , J. 1981 . Thermodynamics of some layered Ising models . Z. Phys. , B44 : 129
   Google Scholar
• Hoever , P. , Wolff , W. F. and Zittartz , J. 1981 . Random layered frustration models . Z. Phys. , B41 : 43
   Google Scholar
• Houtappel , R. M. F. 1950 . Order-disorder in hexagonal lattices . Physica , 16 : 425
   Google Scholar
• Imada , M. 1987 . Thermodynamic properties of spin 1/2 triangular antiferromagnet . J. Phys. Soc. Japan , 56 : 311
   Google Scholar
• Izyumov , Yu. A. 1987 . “ Neutron diffraction on the long-periodic structures ” . In Energoatomizdat 199 Moscow
   Google Scholar
• Izyumov , Yu. A. and Syromyatnikov , V. N. 1984 . Phase transitions and crystal symmetry , 246 Moscow : Nauka .
   Google Scholar
• Jones , D. R. T. , Love , A. and Moore , M. A. 1976 . Phase transitions in superfluid 3He . J. Phys. , C9 : 743
   Google Scholar
• Jose , J. V. , Kadanoff , L. P. , Kirkpatrick , S. and Nelson , D. R. 1977 . Renormalization, vortices and symmetry-breaking perturbations in the two-dimensional planar model . Phys. Rev. , B16 : 1217
   Web of Science ®Google Scholar
• Kadowaki , H. , Ubukoshi , K. , Hirakawa , K. , Martinez , J. L. and Shirane , G. 1987 . Experimental study of new type phase transition in triangular lattice antiferromagnet VCl2 . J. Phys. Soc. Japan , 56 : 4027
   Google Scholar
• Kawamura , H. 1985 . New critical behaviour I. Heisenberg antiferromagnet on the layered-triangular lattice . J. Phys. Soc. Japan , 54 : 3220
   Google Scholar
• Kawamura , H. 1986a . Phase transition of the three-dimensional Xy antiferromagnet on the layeredtriangular lattice . J. Phys. Soc. Japan , 55 : 2095
   Google Scholar
• Kawamura , H. 1986b . Renormalization-group approach to the frustrated Heisenberg antiferromagnet on the layered-triangular lattice . J. Phys. Soc. Japan , 55 : 2157
   Google Scholar
• Kawamura , H. and Miyashita , S. 1984 . Phase transition in the two-dimensional Heisenberg antiferromagnet on the triangular lattice . J. Phys. Soc. Japan , 53 : 4138
   Google Scholar
• Kawamura , H. and Miyashita , S. 1985 . Phase transition of the Heisenberg antiferromagnet on the triangular lattice in a magnetic field . J. Phys. Soc. Japan , 54 : 4530
   Google Scholar
• Khmelnitsky , D. E. 1975 . Phase transition of second order in inhomogeneous bodies . Zh. Eksp. Teor. Fiz. , 68 : 1960
   Google Scholar
• Kirkpatrick , S. 1977 . Low-frequency response functions on random magnetic systems . Phys. Rev. , B16 : 4630
   Google Scholar
• Kogut , J. B. 1979 . An introduction to lattice gauge theory and spin systems . Rev. Mod. Phys. , 51 : 659
   Web of Science ®Google Scholar
• Kosterlitz , J. M. 1974 . The critical properties of the two-dimensional XY model . J. Phys. , C7 : 1046
   Google Scholar
• Kosterlitz , J. M. and Thouless , D. J. 1973 . Ordering, metastability and phase transitions in twodimensional systems . J. Phys. , C6 : 1181
   Google Scholar
• Kuindersma , S. R. , Sanchez , J. P. and Haas , G. 1981 . Magnetic and structural investigations on NiJ2 and CoJ2 . Physica , B111 : 231
   Google Scholar
• Landau , D. P. 1976 . Finite-size behaviour of the cubic Ising lattice . Phys. Rev. , B14 : 255
   Google Scholar
• Landau , D. P. 1977 . Critical behaviour of a bcc Ising antiferromagnet in a magnet field . Phys. Rev. , B16 : 4164
   Google Scholar
• Lee , D. H. , Joannopoulos , J. D. , Negele , J. W. and Landau , D. P. 1984 . Discrete-symmetry breaking and novel critical phenomena in an antiferromagnetic planar (XY) model in two dimensions . Phys. Rev. Lett. , 52 : 433
   Web of Science ®Google Scholar
• Lee , D. H. , Joannopoulos , J. D. , Negele , J. W. and Landau , D. P. 1986 . Symmetry analysis and Monte Carlo study of a frustrated antiferromagnetic planar (XY) model in two dimensions . Phys. Rev. , B33 : 450
   Google Scholar
• Le Guillou , J. C. and Zinn-Justin , J. 1977 . Critical exponents for the n-vector model in three dimensions from field theory . Phys. Rev. Lett. , 39 : 95
   Web of Science ®Google Scholar
• Makrini , M. E. , Guerard , D. , Lagrange , P. and Herord , A. 1980 . Intercalation of rare earth metals in graphite . Physica , B99 : 481
   Google Scholar
• Marland , L. G. and Betts , D. D. 1979 . Frustration effect in quantum spin systems . Phys. Rev. Lett. , 43 : 1628
   Google Scholar
• Matsubara , F. 1982 . Magnetic ordering in a hexagonal antiferromagnet . J. Phys. Soc. Japan , 51 : 2424
   Google Scholar
• Matsubara , F. and Katsura , S. 1977 . High-temperature expansion for the random mixture of the ferromagnetic and antiferromagnetic exchange interaction . J. Phys. , C10 : 4361
   Google Scholar
• McKenzie , S. , Domb , C. and Hunter , D. L. 1982 . Extended high-temperature series for the classical Heisenberg model in three dimensions . J. Phys. , A15 : 3899
   Google Scholar
• Medvedev , M. V. 1978 . Phase diagram of an Ising magnet with random exchange bonds . Phys. Stat. Sol. , B86 : 109
   Google Scholar
• Meier , R. J. and Helmholdt , R. B. 1984 . Neutron diffraction study of α- and β-oxygen . Phys. Rev. , B29 : 1387
   Google Scholar
• Mermin , N. D. 1979 . The topological theory of defects in ordered media . Rev. Mod. Phys. , 51 : 591
   Web of Science ®Google Scholar
• Mihura , B. and Landau , D. P. 1977 . New type of multicritical behaviour in a triangular lattice gas model . Phys. Rev., Lett. , 38 : 977
   Google Scholar
• Miyashita , S. and Kawamura , H. 1985 . Phase transitions of anisotropic Heisenberg antiferromagnets on the triangular lattice . J. Phys. Soc. Japan , 54 : 3385
   Google Scholar
• Miyashita , S. and Shiba , H. 1984 . Nature of the phase transition of the two-dimensional antiferromagnetic plane rotator model on the triangular lattice . J. Phys. Soc. Japan , 33 : 1145
   Google Scholar
• Moore , M. W. , Day , P. , Wilkinson , C. and Ziebeck , K. R. A. 1985 . The effect of iodide doping on the incommensurate helical magnetic structure of NiBr2 . Sol. State Commun. , 53 : 1009
   Google Scholar
• Müller-Hartmann , E. and Zittartz , J. 1977 . Interface free energy and transition temperature of the squarelattice Ising antiferromagnet at finite magnetic field . Z. Phys. , B27 : 261
   Google Scholar
• Nishimori , H. and Miyashita , S. 1986 . Magnetization process of the spin-1/2 antiferromagnetic Ising-like Heisenberg model on the triangular lattice . J. Phys. Soc. Japan , 55 : 4448
   Google Scholar
• Nishimori , H. and Nakanishi , H. 1988 . Ground state of quantum spin systems on the triangular lattice . J. Phys. Soc. Japan , 57 : 626
   Google Scholar
• Oguchi , T. , Nishimori , H. and Taguchi , Y. 1986 . Ground state of antiferromagnetic quantum spin systems on the triangular lattice . J. Phys. Soc. Japan , 55 : 323
   Google Scholar
• Patashinsky , A. Z. and Pokrovsky , V. L. 1982 . Fluctuation theory of phase transition , 256 Moscow : Nauka .
   Google Scholar
• Penrose , R. and Rindler , W. 1984 . Spinors and space-time , 60 – 80 . Cambridge University Press .
   Google Scholar
• Peschel , I. 1982 . On the correlation functions of fully frustrated two-dimensional Ising systems . Z. Phys. , B45 : 339
   Google Scholar
• Petrakovsky , G. A. 1981 . Amorphous magnets . Usp. Fiz. Nauk , 134 : 305
   Google Scholar
• Pfenty , P. 1970 . The one-dimensional Ising model with a transverse field . Ann. Phys. (N.Y.). , 57 : 79
   Google Scholar
• Pikin , S. A. and Tsukernik , V. M. 1966 . On thermodynamics of spin linear chains in transverse field . Zh. Eksp. Teor. Fiz. , 50 : 1377
   Google Scholar
• Plechko , V. N. 1985 . Method of calculations in the two-dimensional Ising systems . Preprint JINR , P17 : 85 – 927 . Dubna
   Google Scholar
• Ponomarev , V. I. 1984 . Critical properties of a one-dimensional interacting Fermi system in a magnetic field . Phys. Lett. , A101 : 361
   Google Scholar
• Ponomarev , V. I. 1984 . Phase transition in magnetic field in one-dimensional fermion systems . Fiz. Met. Metalloved. , 58 : 436
   Google Scholar
• Ponomarev , V. I. , Kontorovitch , V. M. and Tsukernik , V. M. 1973 . Scaling relation for phase transition in one-dimensional spin XY-model . Zh. Eksp. Teor. Fiz. , 65 : 1212
   Google Scholar
• Ponomarev , V. I. and Kuzmin , E. V. 1983 . Cluster model of ferromagnet-spin glass transition . Fiz. Met. Metalloved. , 55 : 65
   Google Scholar
• Ponomarev , V. I. and Kuzmin , E. V. 1984 . Ground state structure and phase transitions in disordered spin system with frustrations . Fiz. Met. Metalloved. , 57 : 1063
   Google Scholar
• Rastelli , E. and Tassi , A. 1986 . The rhombohedral Heisenberg antiferromagnet: infinite degeneracy of the ground state and magnetic properties of solid oxygen. . J. Phys. , C19 : L423
   Google Scholar
• Rastelli , E. and Tassi , A. 1987 . Order produced by quantum disorder in the Heisenberg rhombohedral antiferromagnet . J, Phys. , C20 : L303
   Google Scholar
• Rastelli , E. , Reatto , L. and Tassi , A. 1986 . Neutron scattering in the rhombohedral Heisenberg antiferromagnet: application to β-oxygen. . J. Phys. , C19 : L589
   Google Scholar
• Rushbrooke , G. S. , Baker , G. A. and Wood , P. J. 1974 . Phase Transition and Critical Phenomena . Academic Press , 3 : 245 – 305 .
   Google Scholar
• Sakakibara , T. and Date , M. 1984 . Magnetism of C6Eu. Existence of the four-spin exchange interactions . J. Phys. Soc. Japan , 53 : 3599
   Google Scholar
• Shenker , S. H. and Tobochnik , J. 1980 . Monte Carlo renormalization-group analysis of the classical Heisenberg model in two dimensions . Phys. Rev. , B22 : 4462
   Google Scholar
• Shiba , H. 1982 . Dipole-dipole interaction as a possible origin of incommensurate manetic structures in triangular antiferromagnets . Sol. State Commun. , 41. : 511
   Google Scholar
• Southern , B. W. and Yang , A. P. 1977 . Real space rescaling study of spin glass behaviour in three dimensions . J. Phys. , C10 : 2179
   Google Scholar
• Stephen , M. J. and Mittag , L. 1972 . A new representation of the solution of the Ising model . J. Math. Phys. , 13 : 1944
   Google Scholar
• Stephens , P. W. , Birgeneau , R. J. , Majkrzak , C. F. and Shirane , G. 1983 . Magnetic structure and dynamics in α- and β-phase solid oxygen . Phys. Rev. , B28 : 452
   Google Scholar
• Stephenson , J. 1964 . Ising-model spin correlations on the triangular lattice . J. Math. Phys. , 5 : 1009
   Web of Science ®Google Scholar
• Stephenson , J. 1970 . Ising-model spin correlations on the triangular lattice: III. Isotropic antiferromagnetic lattice; IV. Anisotropic ferromagnetic and antiferromagnetic lattice . J. Math. Phys. , 11 : 413 – 420 .
   Google Scholar
• Sütö , A. 1981 . Models of superfrustration . Z. Phys. , B44 : 121
   Google Scholar
• Syozi , I. 1972 . “ Transformation of Ising model ” . In Phase Transition and Critical Phenomena , Vol. 1 , 269 London : Academic Press .
   Google Scholar
• Takasaki , K. , Harada , I. and Tonegawa , T. 1986 . Magnetic phase diagram of the Ising model on a triangular lattice with antiferromagnetic nearest-neighbor and next-nearest-neighbor interactions . J. Phys. Soc. Japan , 55 : 4423
   Google Scholar
• Takeda , K. , Ubukoshi , K. , Haseda , T. and Hirakawa , K. 1984 . Heat capacities of the two-dimensional triangular antiferromagnets VX2 (X = Cl, Br, I) . J. Phys. Soc. Japan , 53 : 1480
   Google Scholar
• Tobochnik , J. and Chester , G. V. 1979 . Monte Carlo study of the planar spin model . Phys. Rev. , B20 : 3761
   Google Scholar
• Toulouse , G. 1977 . Theory of the frustrated effect in spin glasses . Commun. Phys. , 2 : 115
   Web of Science ®Google Scholar
• Toulouse , G. and Kleman , M. 1976 . Principles of a classification defects in ordered media . J. Phys. Lett. , 37 : 149
   Google Scholar
• Vaks , V. G. and Geilikman , M. B. 1971 . On low temperature and vertual phase transitions . Zh. Eksp. Teor. Fiz. , 60 : 330
   Google Scholar
• Vaks , V. G. , Larkin , A. I. and Ovchinnikov , Y. N. 1965 . Ising model with next-nearest-neighbor interaction . Zh. Eksp. Teor. Fiz. , 49 : 1180
   Google Scholar
• Vaks , V. G. , Zinenko , V. I. and Shneider , V. E. 1983 . Microscopic theory of structural phase transitions order-disorder in crystals . Usp. Fiz. Nauk. , 141 : 629
   Google Scholar
• Villain , J. 1977a . A magnetic analogue of stereoisomerism: applications to Helmagnetism in two dimensions . J. Physique , 38 : 385
   Google Scholar
• Villain , J. 1977b . Helimagnetic-ferromagnetic transition . Physica , B86–88 : 631
   Google Scholar
• Volovik , G. E. and Mineev , V. P. 1976 . Linear and point peculiarities in He3 . Pis'ma Zh. Eksp. Teor. Fiz. , 24 : 605
   Google Scholar
• Wada , N. , Ubukoshi , K. and Hirakawa , K. 1982 . Incommensurate magnetic phase transitions in the triangular XY-like antiferromagnet RbFeCl3 . J. Phys. Soc. Japan , 51 : 2833
   Google Scholar
• Waldor , M. H. , Wolff , W. F. and Zittartz , J. 1984 . Ising model on the pentagon lattice . Phys. Lett. , A106 : 261
   Google Scholar
• Wannier , G. H. 1950 . Antiferromagnetism. The triangular Ising net . Phys. Rev. , 79 : 357
   Web of Science ®Google Scholar
• Wannier , G. H. 1973 . Antiferromagnetism. The triangular Ising net . Phys. Rev. , B7 : 5017
   Google Scholar
• Wilson , K. G. 1974 . Confinement of quarks . Phys. Rev. , D14 : 2455
   Google Scholar
• Wolff , W. F. and Zittartz , J. 1981 . Inhomogeneous Ising models with diagonal structure on square lattice . Z. Phys. , 44 : 109
   Google Scholar
• Wu , F. J. 1982 . The Potts model . Rev. Mod. Phys. , 54 : 235
   Web of Science ®Google Scholar
• Yamada , I. , Ubukoshi , K. and Hirakawa , K. 1984 . ESR study of the triangular lattice Heisenberg antiferromagnets VX2(X = Cl, Br, I) . J. Phys. Soc. Japan , 53 : 381
   Google Scholar
• Yamada , I. , Ubukoshi , K. and Hirakawa , K. 1985 . ESR study of the triangular lattice antiferromagnets with S = 1/2: NaTiO2 and LiNiO2 . J. Phys. Soc. Japan , 54 : 3571
   Google Scholar
• Yosefin , M. and Domany , E. 1985 . Phase transitions in fully frustrated spin systems . Phys, Rev. , B32 : 1778
   Google Scholar