scholarly journals Effective One-Dimensional Coupling in the Highly Frustrated Square-Lattice Itinerant Magnet CaCo2−yAs2

2017 ◽  
Vol 119 (14) ◽  
Author(s):  
A. Sapkota ◽  
B. G. Ueland ◽  
V. K. Anand ◽  
N. S. Sangeetha ◽  
D. L. Abernathy ◽  
...  
Keyword(s):  
Square Lattice ◽  
One Dimensional ◽  
Dimensional Coupling ◽  
Itinerant Magnet

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.

The annihilating process on random trees and the square lattice

2004 ◽  
Vol 41 (3) ◽  
pp. 816-831
Author(s):  
Aidan Sudbury
Keyword(s):  
Survival Probability ◽  
Particle System ◽  
Random Trees ◽  
Interacting Particle System ◽  
Random Tree ◽  
Square Lattice ◽  
One Dimensional ◽  
Interacting Particle

An annihilating process is an interacting particle system in which the only interaction is that a particle may kill a neighbouring particle. Since there is no birth and no movement, once a particle has no neighbours its site remains occupied for ever. The survival probability is calculated for a random tree and for the square lattice. A connection is made between annihilating processes and the adsorption of molecules onto surfaces. A one-dimensional adsorption problem is solved in the case in which the two neighbours do not act independently.

scholarly journals Thermally and field-driven mobility of emergent magnetic charges in square artificial spin ice

2019 ◽  
Vol 9 (1) ◽  
Author(s):  
Sophie A. Morley ◽  
Jose Maria Porro ◽  
Aleš Hrabec ◽  
Mark C. Rosamond ◽  
Diego Alba Venero ◽  
...  
Keyword(s):  
Critical Field ◽  
Magnetic Monopoles ◽  
Model Systems ◽  
Square Lattice ◽  
Creep Model ◽  
Spin Ice ◽  
One Dimensional ◽  
X Ray ◽  
Drift Motion ◽  
Artificial Spin Ice

Abstract Designing and constructing model systems that embody the statistical mechanics of frustration is now possible using nanotechnology. We have arranged nanomagnets on a two-dimensional square lattice to form an artificial spin ice, and studied its fractional excitations, emergent magnetic monopoles, and how they respond to a driving field using X-ray magnetic microscopy. We observe a regime in which the monopole drift velocity is linear in field above a critical field for the onset of motion. The temperature dependence of the critical field can be described by introducing an interaction term into the Bean-Livingston model of field-assisted barrier hopping. By analogy with electrical charge drift motion, we define and measure a monopole mobility that is larger both for higher temperatures and stronger interactions between nanomagnets. The mobility in this linear regime is described by a creep model of zero-dimensional charges moving within a network of quasi-one-dimensional objects.

One-dimensional crystal growth model on a square lattice substrate

2016 ◽  
Vol 380 (37) ◽  
pp. 2989-2992 ◽  
Author(s):  
Yi Cheng ◽  
Chenxi Lu ◽  
Bo Yang ◽  
Xiangming Tao ◽  
Jianfeng Wang ◽  
...  
Keyword(s):  
Crystal Growth ◽  
Growth Model ◽  
Square Lattice ◽  
One Dimensional ◽  
Dimensional Crystal

New exact results for the defective square lattice

1976 ◽  
Vol 80 (2) ◽  
pp. 365-381 ◽  
Author(s):  
G. Ronca
Keyword(s):  
Closed Form Solution ◽  
Exact Result ◽  
Form Solution ◽  
Square Lattice ◽  
Zero Temperature ◽  
Real Crystal ◽  
One Dimensional ◽  
Resonance Modes ◽  
The One ◽  
Dimensional Crystal

Since the publication of the fundamental papers by Lifshitz (1, 2) and Montroll and Potts (3, 4) many authors have investigated the effect of an isotopic impurity on the lattice vibrations of a harmonic crystal at zero temperature. A fairly broad knowledge is now available on scattering amplitudes, localized modes and resonance modes (6, 7). Nevertheless, as pointed out by Maradudin and Montroll (see (7), p. 430), a closed form solution to the problem has been found only for the one-dimensional crystal, the work done on two and three-dimensional crystals being predominantly numerical. Unfortunately the one-dimensional crystal, as an approximation for a real crystal is an oversimplified model, incapable as it is of exhibiting resonance modes. To the author's knowledge the most significant exact result concerning the classical behaviour at zero temperature of crystals having a dimensionality higher than one is the connexion, calculated by Mahanty et al. (5) between localized mode frequency and impurity mass for the case of a square lattice undergoing planar vibrations.

The annihilating process on random trees and the square lattice

2004 ◽  
Vol 41 (03) ◽  
pp. 816-831
Author(s):  
Aidan Sudbury
Keyword(s):  
Survival Probability ◽  
Particle System ◽  
Random Trees ◽  
Interacting Particle System ◽  
Random Tree ◽  
Square Lattice ◽  
One Dimensional ◽  
Interacting Particle

An annihilating process is an interacting particle system in which the only interaction is that a particle may kill a neighbouring particle. Since there is no birth and no movement, once a particle has no neighbours its site remains occupied for ever. The survival probability is calculated for a random tree and for the square lattice. A connection is made between annihilating processes and the adsorption of molecules onto surfaces. A one-dimensional adsorption problem is solved in the case in which the two neighbours do not act independently.

scholarly journals RELAXATION UNDER OUTFLOW DYNAMICS WITH RANDOM SEQUENTIAL UPDATING

2005 ◽  
Vol 16 (11) ◽  
pp. 1771-1783 ◽  
Author(s):  
SYLWIA KRUPA ◽  
KATARZYNA SZNAJD-WERON
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Simulations ◽  
Mean Field ◽  
Square Lattice ◽  
One Dimensional ◽  
Sequential Updating ◽  
The Mean

In this paper we compare the relaxation in several versions of the Sznajd model (SM) with random sequential updating on the chain and square lattice. We start by reviewing briefly all proposed one-dimensional versions of SM. Next, we compare the results obtained from Monte Carlo simulations with the mean field results obtained by Slanina and Lavicka. Finally, we investigate the relaxation on the square lattice and compare two generalizations of SM, one suggested by Stauffer et al. and another by Galam. We show that there are no qualitative differences between these two approaches, although the relaxation within the Galam rule is faster than within the well known Stauffer et al. rule.

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