scholarly journals Two-dimensional Ising model with competing interactions: Phase diagram and low-temperature remanent disorder

2009 ◽  
Vol 79 (1) ◽  
Author(s):  
A. O’Hare ◽  
F. V. Kusmartsev ◽  
K. I. Kugel
Keyword(s):  
Phase Diagram ◽  
Ising Model ◽  
Low Temperature ◽  
Two Dimensional ◽  
Competing Interactions

scholarly journals Phase diagram of the two-dimensional Ising model with random competing interactions

2009 ◽  
Vol 373 (30) ◽  
pp. 2525-2528 ◽  
Author(s):  
Octavio R. Salmon ◽  
J. Ricardo de Sousa ◽  
Fernando D. Nobre
Keyword(s):  
Phase Diagram ◽  
Ising Model ◽  
Two Dimensional ◽  
Competing Interactions

scholarly journals Low-temperature antiferromagnetism of Ising model with competing interactions

2021 ◽  
pp. 64-71
Author(s):  
Kirill Tsiberkin ◽  
Keyword(s):  
Ising Model ◽  
Low Temperature ◽  
Temperature Shift ◽  
Second Order ◽  
Square Lattice ◽  
Antiferromagnetic Coupling ◽  
Competing Interactions ◽  
Saturation State ◽  
Spin Configuration ◽  
Competing Interaction

The paper presents a numerical analysis of equilibrium state and spin configuration of square lattice Ising model with competing interaction. The most detailed description is given for case of ferromagnetic interaction of the first-order neighbours and antiferromagnetic coupling of the second-order neighbours. The numerical method is based on Metropolis algorithm. It uses 128×128 lattice with periodic boundary conditions. At first, the simulation results show that the system is in saturation state at low temperatures, and it turns into paramagnetic state at the Curie point. The competing second-order interaction makes possible the domain structure realization. This state is metastable, because its energy is higher than saturation energy. The domains are small at low temperature, and their size increases when temperature is growing until the single domain occupies the whole simulation area. In addition, the antiferromagnetic coupling of the second-order neighbours reduces the Curie temperature of the system. If it is large enough, the lattice has no saturation state. It turns directly from the domain state into paramagnetic phase. There are no extra phases when the system is antiferromagnetic in main order, and only the Neel temperature shift realizes here.

TWO-DIMENSIONAL WANG–LANDAU SAMPLING OF AN ASYMMETRIC ISING MODEL

2009 ◽  
Vol 20 (09) ◽  
pp. 1357-1366 ◽  
Author(s):  
SHAN-HO TSAI ◽  
FUGAO WANG ◽  
D. P. LANDAU
Keyword(s):  
Phase Diagram ◽  
Ising Model ◽  
External Field ◽  
Density Of States ◽  
Triangular Lattice ◽  
Sampling Method ◽  
Two Dimensional ◽  
Theoretical Predictions ◽  
The Spectator ◽  
Three Body

We study the critical endpoint behavior of an asymmetric Ising model with two- and three-body interactions on a triangular lattice, in the presence of an external field. We use a two-dimensional Wang–Landau sampling method to determine the density of states for this model. An accurate density of states allowed us to map out the phase diagram accurately and observe a clear divergence of the curvature of the spectator phase boundary and of the derivative of the magnetization coexistence diameter near the critical endpoint, in agreement with previous theoretical predictions.

2D ISING MODEL WITH COMPETING INTERACTIONS AND ITS APPLICATION TO CLUSTERS AND ARRAYS OF π-RINGS, GRAPHENE AND ADIABATIC QUANTUM COMPUTING

2009 ◽  
Vol 23 (20n21) ◽  
pp. 3951-3967 ◽  
Author(s):  
ANTHONY O'HARE ◽  
F. V. KUSMARTSEV ◽  
K. I. KUGEL
Keyword(s):  
Quantum Computing ◽  
Ising Model ◽  
Ground State ◽  
Honeycomb Lattice ◽  
Graphene Plane ◽  
Two Dimensional ◽  
Coupling Constant ◽  
Competing Interactions ◽  
Adiabatic Quantum Computing ◽  
Ising Spins

We study the two-dimensional Ising model with competing nearest-neighbour and diagonal interactions and investigate the phase diagram of this model. We show that the ground state at low temperatures is ordered either as stripes or as the Néel antiferromagnet. However, we also demonstrate that the energy of defects and dislocations in the lattice is close to the ground state of the system. Therefore, many locally stable (or metastable) states associated with local energy minima separated by energy barriers may appear forming a glass-like state. We discuss the results in connection with two physically different systems. First, we deal with planar clusters of loops including a Josephson π-junction (a π-rings). Each π-ring carries a persistent current and behaves as a classical orbital moment. The type of particular state associated with the orientation of orbital moments in the cluster depends on the interaction between these orbital moments and can be easily controlled, i.e. by a bias current or by other means. Second, we apply the model to the analysis of the structure of the newly discovered two-dimensional form of carbon, graphene. Carbon atoms in graphene form a planar honeycomb lattice. Actually, the graphene plane is not ideal but corrugated. The displacement of carbon atoms up and down from the plane can be also described in terms of Ising spins, the interaction of which determines the complicated shape of the corrugated graphene plane. The obtained results may be verified in experiments and are also applicable to adiabatic quantum computing where the states are switched adiabatically with the slow change of coupling constant.

Phase diagram for the striped phase in the two-dimensional dipolar Ising model

1996 ◽  
Vol 54 (5) ◽  
pp. 3394-3402 ◽  
Author(s):  
J. Arlett ◽  
J. P. Whitehead ◽  
A. B. MacIsaac ◽  
K. De’Bell
Keyword(s):  
Phase Diagram ◽  
Ising Model ◽  
Two Dimensional

Phase Transition in 2D Anisotropic Ising Model with Next-Nearest Neighbor Interactions in a Magnetic Field

SPIN ◽  
2018 ◽  
Vol 08 (03) ◽  
pp. 1850010
Author(s):  
D. Farsal ◽  
M. Badia ◽  
M. Bennai
Keyword(s):  
Magnetic Field ◽  
Phase Transition ◽  
Phase Diagram ◽  
Monte Carlo ◽  
Magnetic Susceptibility ◽  
Critical Temperature ◽  
Ising Model ◽  
Nearest Neighbor ◽  
Two Dimensional ◽  
The Magnetic Field

The critical behavior at the phase transition of the ferromagnetic two-dimensional anisotropic Ising model with next-nearest neighbor (NNN) couplings in the presence of the field is determined using mainly Monte Carlo (MC) method. This method is used to investigate the phase diagram of the model and to verify the existence of a divergence at null temperature which often appears in two-dimensional systems. We analyze also the influence of the report of the NNN interactions [Formula: see text] and the magnetic field [Formula: see text] on the critical temperature of the system, and we show that the critical temperature depends on the magnetic field for positive values of the interaction. Finally, we have investigated other thermodynamical qualities such as the magnetic susceptibility [Formula: see text]. It has been shown that their thermal behavior depends qualitatively and quantitatively on the strength of NNN interactions and the magnetic field.

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