Statistical mechanics of the two-dimensional assembly

1950 ◽  
Vol 202 (1069) ◽  
pp. 202-207 ◽  
Keyword(s):  
Ising Model ◽  
Curie Temperature ◽  
Statistical Mechanics ◽  
Specific Heat ◽  
Considerable Effect ◽  
Square Lattice ◽  
Nearest Neighbour ◽  
Two Dimensional ◽  
Triangular Lattices

The work of Kaufman & Onsager (1946) on the two-dimensional Ising model of a ferromagnet is extended from the plane square lattice to the plane honeycomb and triangular lattices. The specific heat anomaly, where it exists, turns out to be of the same type in all three lattices, an infinity in the specific heat at the Curie temperature. It is concluded that second-nearest neighbour interactions may have a considerable effect on the position of the Curie temperature.

Specific heat of ordered and isotopically disordered lattices

1978 ◽  
Vol 56 (10) ◽  
pp. 1390-1394
Author(s):  
K. P. Srivastava
Keyword(s):  
Specific Heat ◽  
Low Temperatures ◽  
Numerical Study ◽  
Three Dimensional ◽  
Constant Volume ◽  
Nearest Neighbour ◽  
Two Dimensional ◽  
Appreciable Difference ◽  
Substantial Change ◽  
Neighbour Interaction

An extensive numerical study on specific heat at constant volume (Cv) for ordered and isotopically disordered lattices has been made. Cv at various temperatures for ordered and disordered linear and two-dimensional lattices have been compared and no appreciable difference in Cv between these two structures has been observed. Effect of concentration of light atoms on Cv for three-dimensional isotopically disordered lattices has also been shown.In spite of taking next-nearest-neighbour interaction into account, no substantial change in Cv between the ordered and isotopically disordered linear lattices has been found. It is shown that the low lying modes contribute substantially at low temperatures.

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.

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.

KNOTTED VORTICES AND SUPERFLUID PHASE TRANSITION

1993 ◽  
Vol 07 (23) ◽  
pp. 1523-1526 ◽  
Author(s):  
ROBERT OWCZAREK
Keyword(s):  
Phase Transition ◽  
Ising Model ◽  
Specific Heat ◽  
Superfluid Helium ◽  
Vortex Structures ◽  
Two Dimensional ◽  
Superfluid Phase ◽  
Λ Point

In this letter, studies of knotted vortex structures in superfluid helium are continued. A model of superfluid phase transition (λ-transition) is built in this framework. Similarities of this model to the two-dimensional Ising model are shown. Dependence of specific heat of superfluid helium on temperature near the λ point is explained.

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.

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