Dislocations and crowdions in two-dimensional crystals. I. Atomic-lattice models and a continuum description of these defects in elastic anisotropic 2D media

2014 ◽  
Vol 40 (12) ◽  
pp. 1063-1076 ◽  
Author(s):  
V. D. Natsik ◽  
S. N. Smirnov
Keyword(s):  
Lattice Models ◽  
Two Dimensional ◽  
Atomic Lattice ◽  
Continuum Description

scholarly journals On the determination of step energies. Theoretical considerations and application to an anisotropic Kossel model

2006 ◽  
Vol 39 (4) ◽  
pp. 563-570 ◽  
Author(s):  
M. A. Deij ◽  
J. H. Los ◽  
H. Meekes ◽  
E. Vlieg
Keyword(s):  
Lattice Models ◽  
Single Step ◽  
Spiral Growth ◽  
Growth Theory ◽  
Two Dimensional ◽  
Island Growth ◽  
Growth Step ◽  
Step Flow ◽  
Theoretical Considerations

Steps on surfaces are important in crystal growth theory, as the step free energy determines the two-dimensional nucleation rate, island growth, step flow and spiral growth. In this paper, it is illustrated that in general in lattice models the step energy of a single step cannot be determined directly by counting broken bonds. A new method is proposed that uses the geometry of a step together with the bonding topology, allowing for a straightforward determination of single-step energies for any case. The method is applied to an anisotropic Kossel model.

Tunable optical vortex array in a two-dimensional electromagnetically induced atomic lattice

2021 ◽  
Author(s):  
jinpeng Yuan ◽  
Hengfei ZHANG ◽  
Chaohua Wu ◽  
lirong wang ◽  
liantuan xiao ◽  
...  
Keyword(s):  
Optical Vortex ◽  
Two Dimensional ◽  
Atomic Lattice ◽  
Vortex Array

scholarly journals GENERALIZED YANG-BAXTER EQUATION

1993 ◽  
Vol 08 (24) ◽  
pp. 2299-2309 ◽  
Author(s):  
R. M. KASHAEV ◽  
YU. G. STROGANOV
Keyword(s):  
Single Layer ◽  
Lattice Models ◽  
Baxter Equation ◽  
Explicit Solutions ◽  
Generalized Equations ◽  
Two Dimensional ◽  
Layer Transfer ◽  
Transfer Matrices ◽  
Dimensional Lattice ◽  
Potts Models

A generalization of the Yang-Baxter equation is proposed. It enables us to construct integrable two-dimensional lattice models with commuting two-layer transfer matrices, while single-layer ones are not necessarily commutative. Explicit solutions to the generalized equations are found. They are related with Boltzmann weights of the sl (3) chiral Potts models.

scholarly journals Cluster Structure of Optimal Solutions in Bipartitioning of Small Worlds

Entropy ◽  
2020 ◽  
Vol 22 (11) ◽  
pp. 1319
Author(s):  
Adam Lipowski ◽  
António L. Ferreira ◽  
Dorota Lipowska
Keyword(s):  
Cluster Structure ◽  
Finite Size ◽  
Lattice Models ◽  
Square Lattice ◽  
Dimensional Case ◽  
Two Dimensional ◽  
Small Worlds ◽  
Replica Symmetry ◽  
One Dimensional ◽  
Optimal Partitions

Using simulated annealing, we examine a bipartitioning of small worlds obtained by adding a fraction of randomly chosen links to a one-dimensional chain or a square lattice. Models defined on small worlds typically exhibit a mean-field behavior, regardless of the underlying lattice. Our work demonstrates that the bipartitioning of small worlds does depend on the underlying lattice. Simulations show that for one-dimensional small worlds, optimal partitions are finite size clusters for any fraction of additional links. In the two-dimensional case, we observe two regimes: when the fraction of additional links is sufficiently small, the optimal partitions have a stripe-like shape, which is lost for a larger number of additional links as optimal partitions become disordered. Some arguments, which interpret additional links as thermal excitations and refer to the thermodynamics of Ising models, suggest a qualitative explanation of such a behavior. The histogram of overlaps suggests that a replica symmetry is broken in a one-dimensional small world. In the two-dimensional case, the replica symmetry seems to hold, but with some additional degeneracy of stripe-like partitions.

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