The (k B T C/zJ,k) Phase Diagram for the D/J=1 on the Four-Dimensional Blume–Emery–Griffiths (BEG) Model

We theoretically investigate the fcc(110) surfaces with missing row reconstructions induced by adatoms using the Blume–Emmery–Griffith (BEG) model. In the model, Kij is introduced to denote interactions between surface atoms and Jij to describe interactions between dipoles. The investigation by the mean field approximation has predicted that there appear modulated phases on the surfaces as the next-nearest-neighbor (NNN) and the nearest-neighbor (NN) interactions along the [001] direction become competitive. In this study, Monte Carlo simulations are performed to confirm the prediction. A correlation function defined by concentration operators in wave vector q space is calculated. The results show that the concentration modulations appear. The temperature versus the ratio of the NNN interaction K2 to the NN interaction K1 phase diagram is obtained. The possible features of the modulated phases in experiments are discussed.

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THEORETICAL ANALYSIS OF ADSORBATE-INDUCED ROW-TYPE ALIGNMENTS ON THE FCC(110) SURFACE

Surface Review and Letters ◽

10.1142/s0218625x99000688 ◽

1999 ◽

Vol 06 (05) ◽

pp. 699-704 ◽

Cited By ~ 4

Author(s):

K. YASUTANI ◽

M. KABURAGI ◽

M. KANG

Keyword(s):

Phase Diagram ◽

Theoretical Analysis ◽

Ground State ◽

Nearest Neighbor ◽

Comparison Method ◽

Model Structure ◽

Two Dimensional ◽

Ground State Phase Diagram ◽

Interaction Regime ◽

Beg Model

The structures of adsorbate-induced row-type alignments of the FCC(110) surface are analyzed using the two-dimensional Blume–Emmery–Griffiths (BEG) model with the nearest-neighbor (NN) and the next-nearest-neighbor (NNN) interactions. The ground state phase diagram in whole regimes of interactions is determined by the energy comparison method. Comparing the results of ground state analysis with experimentally observed structures of the O/Rh(110) and O/Pd(110), we determine the interaction regimes for these systems. From the thus determined interaction regime, we propose the model structure in the c(2 × 6) phase of the O/Pd(110).

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Phase diagram of a spin-1 magnetic bilayer by cluster variational theory: Exact results for a BEG model on a Bethe lattice with five-fold coordination

Journal of Magnetism and Magnetic Materials ◽

10.1016/s0304-8853(98)00136-x ◽

1998 ◽

Vol 187 (3) ◽

pp. 381-392 ◽

Cited By ~ 58

Author(s):

J.W. Tucker ◽

T. Balcerzak ◽

M. Gzik ◽

A. Sukiennicki

Keyword(s):

Phase Diagram ◽

Bethe Lattice ◽

Exact Results ◽

Variational Theory ◽

Beg Model

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PHASE DIAGRAM OF ADSORBATE-INDUCED ROW-TYPE ALIGNMENTS

Surface Review and Letters ◽

10.1142/s0218625x99000676 ◽

1999 ◽

Vol 06 (05) ◽

pp. 691-697 ◽

Cited By ~ 4

Author(s):

M. KANG ◽

K. YASUTANI ◽

M. KABURAGI

Keyword(s):

Phase Diagram ◽

High Temperatures ◽

Nearest Neighbor ◽

Chemical Potential ◽

Mean Field ◽

Field Approximation ◽

Mean Field Approximation ◽

Dipole Interactions ◽

Beg Model ◽

Incommensurate Phases

The phase diagram of adsorbate-induced row-type alignments, such as missing-row reconstructions induced by adsorbate atoms on the FCC(110) surface, is calculated by the Blume–Emmery–Griffiths (BEG) model. In the model, we introduce adatom–adatom and dipole–dipole interactions between nearest-neighbor (NN) and next-nearest-neighbor (NNN) rows. The calculation of the temperature versus adatom chemical potential phase diagram is performed using mean-field approximation. It is indicated that when NN and NNN interactions are competitive, there appear either dipole or coverage modulated (incommensurate) phases at high temperatures for a wide regime of the interactions.

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PHASE DIAGRAMS OF 3-MATRIX MODEL

Modern Physics Letters A ◽

10.1142/s0217732390002808 ◽

1990 ◽

Vol 05 (29) ◽

pp. 2431-2438 ◽

Cited By ~ 7

Author(s):

KENJI FUKAZAWA ◽

KEN-JI HAMADA ◽

HARUTADA SATO

Keyword(s):

Phase Diagram ◽

Critical Point ◽

Matrix Model ◽

Lattice Gas ◽

Coulomb Gas ◽

Polynomial Method ◽

Chain Model ◽

Random Surface ◽

Spin Ordering ◽

Beg Model

We study the phase diagram of the 3-matrix model. This model corresponds to the Blume-Emery-Griffiths (BEG) model on a random surface. The BEG model has parameters J and K which are the spin and the lattice-gas coupling respectively. If K = 0, it is the usual tri-critical Ising model. If K/J = 3, this model becomes the 3-state Potts model. These models are solved in the context of the Coulomb gas representation. The intermediate region K/J = 1 is equivalent to the 3-matrix chain model and we can solve it exactly using the orthogonal polynomial method. We find the 3rd order critical line on which the spin ordering phase transition occurs. This line ends at the 4th order critical point which corresponds to the tri-critical point of the BEG model. The phase diagram is quite similar to that of the BEG model on a regular lattice.

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