RANDOMLY DECORATED ISING MODEL

1991 ◽  
Vol 05 (04) ◽  
pp. 675-683 ◽  
Author(s):  
L.L. GONÇALVES
Keyword(s):  
Phase Diagram ◽  
Ising Model ◽  
Exchange Interaction ◽  
Discrete Distribution ◽  
Square Lattice ◽  
Two Dimensional ◽  
Percolation Thresholds ◽  
Ising Spins

A study of the two-dimensional (square lattice) randomly decorated Ising model is presented. The bonds are decorated with Ising spins of magnitude s and an annealed discrete distribution [Formula: see text] for the exchange interaction of the decorating bonds is considered. The phase diagram is exactly obtained and for the case where competition is present there are two percolation thresholds, namely, [Formula: see text] which are independent of s. Reentrant behaviour is presented by the system and the region in the space parameters where it occurs is discussed.

scholarly journals Phase transitions of antiferromagnetic Ising spins on the zigzag surface of an asymmetrical Husimi lattice

2019 ◽  
Vol 6 (3) ◽  
pp. 181500 ◽  
Author(s):  
Ran Huang ◽  
Purushottam D. Gujrati
Keyword(s):  
Phase Transitions ◽  
Ising Model ◽  
Spontaneous Magnetization ◽  
Square Lattice ◽  
Two Dimensional ◽  
Simple Formulation ◽  
First Order ◽  
Husimi Lattice ◽  
Antiferromagnetic Ising Model ◽  
Ising Spins

An asymmetrical two-dimensional Ising model with a zigzag surface, created by diagonally cutting a regular square lattice, has been developed to investigate the thermodynamics and phase transitions on surface by the methodology of recursive lattice, which we have previously applied to study polymers near a surface. The model retains the advantages of simple formulation and exact calculation of the conventional Bethe-like lattices. An antiferromagnetic Ising model is solved on the surface of this lattice to evaluate thermal properties such as free energy, energy density and entropy, from which we have successfully identified a first-order order–disorder transition other than the spontaneous magnetization, and a secondary transition on the supercooled state indicated by the Kauzmann paradox.

scholarly journals Neural Network for Prediction of Curie Temperature of Two-Dimensional Ising Model

2021 ◽  
Vol 21 (1) ◽  
pp. 51-60
Author(s):  
A.O. Korol ◽  
◽  
V.Yu. Kapitan ◽  
◽  
◽  
...  
Keyword(s):  
Neural Network ◽  
Ising Model ◽  
Curie Temperature ◽  
High Temperature Phase ◽  
Square Lattice ◽  
Temperature Phase ◽  
The Neural Network ◽  
Different Temperatures ◽  
Low Temperature Phase ◽  
Ising Spins

The authors describe a method for determining the critical point of a second-order phase transitions using a convolutional neural network based on the Ising model on a square lattice. Data for training were obtained using Metropolis algorithm for different temperatures. The neural network was trained on the data corresponding to the low-temperature phase, that is a ferromagnetic one and high-temperature phase, that is a paramagnetic one, respectively. After training, the neural network analyzed input data from the entire temperature range: from 0.1 to 5.0 (in dimensionless units) and determined (the Curie temperature T_c). The accuracy of the obtained results was estimated relative to the Onsager solution for a flat lattice of Ising spins.

THE SIMULATION OF 2D SPIN-1 ISING MODEL WITH POSITIVE BIQUADRATIC INTERACTION ON A CELLULAR AUTOMATON

2003 ◽  
Vol 14 (10) ◽  
pp. 1305-1320 ◽  
Author(s):  
BÜLENT KUTLU
Keyword(s):  
Phase Transition ◽  
Ising Model ◽  
Cellular Automaton ◽  
Intermediate Phase ◽  
Finite Size ◽  
Square Lattice ◽  
Two Dimensional ◽  
Finite Size Scaling ◽  
Creutz Cellular Automaton ◽  
Antiferromagnetic Spin

The two-dimensional antiferromagnetic spin-1 Ising model with positive biquadratic interaction is simulated on a cellular automaton which based on the Creutz cellular automaton for square lattice. Phase diagrams characterizing phase transition of the model are presented for a comparison with those obtained from other calculations. We confirm the existence of the intermediate phase observed in previous works for some values of J/K and D/K. The values of the static critical exponents (β, γ and ν) are estimated within the framework of the finite-size scaling theory for D/K<2J/K. Although the results are compatible with the universal Ising critical behavior in the region of D/K<2J/K-4, the model does not exhibit any universal behavior in the interval 2J/K-4<D/K<2J/K.

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.

A CORRELATION BETWEEN PERCOLATION MODEL AND ISING MODEL

1996 ◽  
Vol 07 (04) ◽  
pp. 609-612 ◽  
Author(s):  
R. HACKL ◽  
I. MORGENSTERN
Keyword(s):  
Critical Temperature ◽  
Ising Model ◽  
Percolation Threshold ◽  
Higher Dimensions ◽  
Percolation Model ◽  
Critical Values ◽  
Square Lattice ◽  
Approximation Formula ◽  
Two Dimensional

In this article we will expose a connection between critical values of percolation and Ising model, i.e., the percolation threshold pc, and the critical temperature Tc and energy Ec, respectively, by the approximation [Formula: see text]. For the two-dimensional square lattice even the identity holds. For higher dimensions — up to d = 7 — and other lattice types we find remarkably small differences from one to five percent.

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 CRITICAL DYNAMICS OF TWO-REPLICA CLUSTER ALGORITHMS

2001 ◽  
Vol 12 (02) ◽  
pp. 257-271
Author(s):  
X.-N. LI ◽  
J. MACHTA
Keyword(s):  
Ising Model ◽  
Critical Behavior ◽  
Cluster Algorithm ◽  
The Other ◽  
Square Lattice ◽  
Critical Dynamics ◽  
Two Dimensional ◽  
Cluster Algorithms ◽  
Dynamic Exponent

The dynamic critical behavior of the two-replica cluster algorithm is studied. Several versions of the algorithm are applied to the two-dimensional, square lattice Ising model with a staggered field. The dynamic exponent for the full algorithm is found to be less than 0.4. It is found that odd translations of one replica with respect to the other together with global flips are essential for obtaining a small value of the dynamic exponent.

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
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