scholarly journals Ground-state and domain-wall energies in the spin-glass region of the two-dimensional±Jrandom-bond Ising model

2007 ◽  
Vol 75 (17) ◽  
Author(s):  
Ronald Fisch ◽  
Alexander K. Hartmann
Keyword(s):  
Ising Model ◽  
Domain Wall ◽  
Spin Glass ◽  
Ground State ◽  
Two Dimensional

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.

scholarly journals Disorder, order, and domain wall roughening in the two-dimensional random field Ising model

1998 ◽  
Vol 58 (5) ◽  
pp. R5217-R5220 ◽  
Author(s):  
E. T. Seppälä ◽  
V. Petäjä ◽  
M. J. Alava
Keyword(s):  
Ising Model ◽  
Domain Wall ◽  
Random Field ◽  
Two Dimensional ◽  
Random Field Ising Model
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