Walk of a Point Defect in a Model with Macroscopic Ground State Degeneracy

1997 ◽  
Vol 11 (07) ◽  
pp. 293-296 ◽  
Author(s):  
A. V. Bakaev ◽  
V. I. Kabanovich
Keyword(s):  
Point Defect ◽  
Ground State ◽  
State Energy ◽  
Hard Spheres ◽  
Three Dimensional ◽  
Lattice Models ◽  
Dimensional Lattice ◽  
Cubic Lattices ◽  
Ground State Degeneracy ◽  
Antiferromagnetic Potts Model

Walks of the point defect in the two- and three-dimensional lattice models of colored hard spheres mimicking the q-state antiferromagnetic Potts model are considered. The walks are generated by moves of neighboring vertices which conserve the ground state energy. Various "traps" confining the walks are observed, while for the models with q≥4 and q≥5 on the square and cubic lattices respectively nonvanishing probabilities that all lattice vertices are attainable in a walk are found.

Solvable Three-Dimensional Lattice Models

1963 ◽  
Vol 132 (3) ◽  
pp. 1085-1092 ◽  
Author(s):  
Bruce W. Knight ◽  
Gerald A. Peterson
Keyword(s):  
Three Dimensional ◽  
Lattice Models ◽  
Dimensional Lattice

EFFECTS OF THE NEXT-NEAREST-NEIGHBOR HOPPING IN OPTICAL LATTICES

2008 ◽  
Vol 22 (01) ◽  
pp. 33-44 ◽  
Author(s):  
YUN'E GAO ◽  
FUXIANG HAN
Keyword(s):  
Phase Diagram ◽  
Hubbard Model ◽  
Ground State Energy ◽  
Ground State ◽  
Optical Lattices ◽  
State Energy ◽  
Nearest Neighbor ◽  
Three Dimensional ◽  
Dispersion Relations ◽  
Insulating Phase

Introducing the next-nearest-neighbor hopping t′ into the Bose–Hubbard model, we study its effects on the phase diagram, on the ground-state energy, and on the quasiparticle and quasihole dispersion relations of the Mott insulating phase in optical lattices. We have found that a negative value of t′ enlarges the Mott-insulating region on the phase diagram, while a positive value of t′ acts oppositely. We have also found that the effects of t′ are dependent on the dimensionality of optical lattices with its effects largest in three-dimensional optical lattices.

Zero-Point Effects in Heisenberg Antiferromagnets with Arbitrary Range of Interaction

1972 ◽  
Vol 50 (23) ◽  
pp. 2991-2996 ◽  
Author(s):  
M. F. Collins ◽  
V. K. Tondon
Keyword(s):  
Ground State ◽  
State Energy ◽  
Correction Term ◽  
Zero Point ◽  
Face Centered Cubic ◽  
Heisenberg Antiferromagnet ◽  
Body Centered Cubic ◽  
Cubic Lattices ◽  
Simple Cubic ◽  
Face Centered

The ground state energy, spin-wave energy, and sublattice magnetization have been calculated for a Heisenberg antiferromagnet at the absolute zero of temperature. The treatment extends the earlier work of Anderson, Kubo, and Oguchi to apply for any two-sublattice antiferromagnet with arbitrary range of interaction. It is shown that for each exchange interaction there is a different characteristic correction term to the energies. Explicit calculations are made of these terms for the simple cubic, body-centered cubic, and face-centered cubic lattices, with both first- and second-neighbor interactions. Applications are also made to NiO and MnO. An extra term in the magnetization series beyond that given by earlier workers is derived.

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