Group-theoretical methods applied to surface problems

References

• Ashkin , J. and Teller , E. 1943 . Statistics of two-dimensional lattices with four components . Phys. Rev. , 64 : 178
   Google Scholar
• Bak , P. 1979 . Surface reconstruction: A physical realization of two-dimensional Ising and XY-models . Solid State Commun. , 32 : 581
   Google Scholar
• Baxter , R. J. 1971 . Eight vertex model in lattice statistics . Phys. Rev. Lett. , 26 : 832
   Google Scholar
• Baxter , R. J. 1973 . Potts model at the critical temperature . J. Phys. C , 6 : L445
   Web of Science ®Google Scholar
• Birman , J. L. 1966 . Simplified theory of symmetry change in second-order phase transitions: Application to V3Si . Phys. Rev. Lett. , 17 : 1216
   Web of Science ®Google Scholar
• Birman , J. L. 1982 . Selection rules for symmetry breaking and symmetry restoration in continuous transitions . Physica , 114A : 564
   Google Scholar
• Blakeley , D. W. and Somorjai , G. A. 1977 . The stability and structure of high Miller index platinum crystal surfaces in vacuum and in the presence of absorbed carbon and oxygen . Surf. Sci. , 65 : 419
   Google Scholar
• Bradley , C. J. and Cracknell , A. P. 1972 . The Mathematical Theory of Symmetry in Solids , Oxford : Clarendon .
   Google Scholar
• Chan , C. M. , Luke , K. L. , Van Hove , M. A. , Weinberg , W. H. and Withrow , S. P. 1978 . The structure of the C(2 × 2) oxygen overlayer on the unreconstructed (110) surface of iridium . Surf. Sci. , 78 : 386
   Google Scholar
• Cracknell , A. P. 1974 . Tables of the irreducible representations of the 17 two-dimensional space groups and their relevance to quantum mechanical eigenstates for surfaces and thin films . Thin Solid Films , 21 : 107
   Google Scholar
• Debe , M. K. and King , D. A. 1977 . Space-group determination of the low-temperature W{001} (√2 × √2)R45° surface structure by low-energy-electron diffraction . Phys. Rev. Lett. , 39 : 708
   Google Scholar
• Deonarine , S. and Birman , J. L. 1983a . Symmetry change in continuous phase transitions in two-dimensional systems . Phys. Rev. B , 27 : 2855
   Google Scholar
• Deonarine , S. and Birman , J. L. 1983b . Group-subgroup phase transitions, Hermann's space-group decomposition theorem, and chain subduction criterion in crystals . Phys. Rev. B , 27 : 4261
   Google Scholar
• Domany , E. and Reidel , E. 1978a . Phase transitions in two-dimensional systems . J. Appl. Phys. , 49 : 1315
   Google Scholar
• Domany , E. , Schick , M. , Walker , J. S. and Griffiths , R. B. 1978 . Classification of continuous order-disorder transitions in adsorbed monolayers . Phys. Rev. B , 18 : 2209
   Google Scholar
• Domany , E. and Schick , M. 1979 . Classification of continuous order-disorder transitions in adsorbed monolayers. II . Phys. Rev. B , 20 : 3828
   Google Scholar
• Felter , T. E. , Barker , R. A. and Estrup , P. J. 1977 . Phase transition on Mo(100) and W(100) surfaces . Phys. Rev. Lett. , 38 : 1138
   Web of Science ®Google Scholar
• Goshen , S. , Mukamel , D. and Shtrikman , S. 1974 . Symmetry changes at phase transitions according to the Landau theory . Int. J. Magnetism , 6 : 221
   Google Scholar
• Hatch , D. M. and Stokes , H. T. 1984 . Symmetry-restricted phase transitions in two-dimensional solids . Phys. Rev. B , 30 : 5156
   Google Scholar
• Hatch , D. M. and Stokes , H. T. 1985 . Practical algorithm for identifying subgroups of space groups . Phys. Rev. B , 31 : 2908
   Google Scholar
• Hatch , D. M. and Stokes , H. T. 1986 . Phase transitions and renormalization group Hamiltonian densities in the 80 diperiodic space groups . Phase Transitions , 7 : 87
   Google Scholar
• Henry , N. F. M. and Lonsdale , K. 1965 . International Tables for X-ray Crystallography , Vol. I. , Kynoch, Birmingham : Symmetry Groups .
   Google Scholar
• Hermann , C. 1929 . Systematic structure theory. IV. Subgroups . Z. Kristallogr. Kristallgeom , 69 : 533
   Google Scholar
• Herring , C. 1937 . Effect of time-reversal symmetry on energy bands of crystals . Phys. Rev. , 52 : 361
   Google Scholar
• Herring , C. 1942 . Character tables for two space groups . J. Franklin Inst. , 233 : 525
   Google Scholar
• Ipatova , I. P. and Kitaev , Yu. E. 1985 . Landau theory of second-order phase transitions on solid surfaces . Prog. Surf. Sci. , 18 : 189
   Google Scholar
• Jarić , M. V. and Birman , J. L. 1977 . Group theory of phase transitions in A-15 (Pm3m) structure . Phys. Rev. B , 16 : 2564
   Google Scholar
• Jose , J. , Kadanoff , L. P. , Kirkpatrick , S. and Nelson , D. R. 1977 . Renormalization, vortices, and symmetry-breaking perturbations in the two-dimensional planar model . Phys. Rev. B , 16 : 1217
   Web of Science ®Google Scholar
• Kociński , J. 1983 . Theory of Symmetry Changes at Continuous Phase Transitions , Amsterdam-Oxford-New York : Elsevier .
   Google Scholar
• van Leeuven , J. M. J. 1975 . Singularities in the critical surface and universality for Ising-like spin systems . Phys. Rev. Lett. , 34 : 1056
   Google Scholar
• Landau , L. D. 1937 . On the theory of phase transitions . Zh. Eksp. Teor. Fiz. , 7 : 19
   Google Scholar
• Landau , L. D. and Lifshitz , E. M. 1980 . Statistical Physics, , 3rd Ed. , New York : Pergamon .
   Google Scholar
• Lifshitz , E. M. 1942 . On the theory of phase transitions of second order . J. Phys. , 6 : 61
   Google Scholar
• Lyubarskii , G. Ya. 1960 . The Application of Group Theory in Physics , New York : Pergamon .
   Google Scholar
• Maksimov , L. A. , Polishchuk , I. Ya. and Somenkow , V. A. 1982 . Complete classification of second-order phase transitions in two-dimensional systems . Solid State Commun. , 44 : 163
   Google Scholar
• Mukamel , D. and Krinsky , S. 1976 . Physical realizations of n  4-component vector models. I. Derivation of the Landau-Ginzburg-Wilson Hamiltonians . Phys. Rev. B , 13 : 5065
   Google Scholar
• Nelson , D. R. and Kosterlit , J. M. 1977 . Universal jump in the superfluid density of two-dimensional superfluids . Phys. Rev. Lett. , 39 : 1201
   Web of Science ®Google Scholar
• Nelson , D. R. and Pelcovits , R. A. 1977 . Momentum-shell recursion relations, an-isotropic spins, and liquid crystals in 2 + ∊ dimensions . Phys. Rev. B , 16 : 2191
   Web of Science ®Google Scholar
• Rottman , C. 1981 . Symmerty classifcation of continuous phase transitions in two dimensions . Phys. Rev. B , 24 : 1482
   Google Scholar
• Straley , J. P. and Fisher , M. E. 1973 . Three-state Potts model and anomalous tricritical points . J. Phys. A , 6 : 1310
   Google Scholar
• Wigner , E. P. 1932 . On the operation of time reversal in quantum mechanics . Nachr. Akad. Wiss. Goettingen, Math.-Phys. , K1 : 546
   Google Scholar
• Wu , F. Y. 1975 . Spontaneous magnetization of the three-spin Ising model on the Union Jack lattice . J. Phys. C , 8 : 2262
   Google Scholar
• Ying , S. C. and Roelofs , L. D. 1983 . Structural phase transition on W and Mo surfaces . Surf. Sci. , 125 : 218
   Google Scholar
• Yonehara , K. and Schmidt , L. D. 1971 . A LEED study of structures produced by H2 on (100) W . Surf. Sci. , 25 : 238
   Web of Science ®Google Scholar
• Zia , R. K. P. and Wallace , D. J. 1975 . Critical behaviour of the continuous n-component Potts model . J. Phys. A , 8 : 1495
   Google Scholar