SERIES EXPANSIONS FOR THE ISING MODEL COUPLED TO TWO HEAT BATHS

1995 ◽  
Vol 09 (24) ◽  
pp. 3181-3188 ◽  
Author(s):  
A. V. BAKAEV ◽  
V. I. KABANOVICH
Keyword(s):  
Ising Model ◽  
Square Lattice ◽  
Series Expansions ◽  
Temperature Ratio ◽  
Spin Models ◽  
High Temperature Expansion ◽  
Different Temperatures ◽  
Lattice Spin Models ◽  
Good Agreement ◽  
Non Equilibrium

We present an algorithm for generating high- and low-temperature expansions for non-equilibrium steady states in lattice spin models coupled to two thermal baths at different temperatures. For the Ising model on a square lattice with the sublattice temperature ratio α = Ta/Tb we construct the high-temperature expansion of energy to order eleven. The estimates of T c are in good agreement with the exact equilibrium result (at α = 1) and the existing Monte-Carlo simulations in non equilibrium cases (α = 2 and α = ∞).

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.

TWO-TEMPERATURE NON-EQUILIBRIUM ISING MODELS

1996 ◽  
Vol 07 (03) ◽  
pp. 389-399 ◽  
Author(s):  
P. TAMAYO ◽  
R. GUPTA ◽  
F. J. ALEXANDER
Keyword(s):  
Ising Model ◽  
Computational Study ◽  
Heat Bath ◽  
Universality Class ◽  
Ising Models ◽  
Local Competition ◽  
Equilibrium Dynamics ◽  
Different Temperatures ◽  
Two Temperature ◽  
Non Equilibrium

We present results from a computational study of a class of 2D two-temperature non-equilibrium Ising models. In these systems the dynamics is a local competition of two equilibrium dynamics at different temperatures. We analyzed non-equilibrium versions of Metropolis, heat bath/Glauber and Swendsen-Wang dynamics and found strong evidence that some of these dynamics have the same critical exponents and belong to the same universality class as the equilibrium 2D Ising model.

LOW-TEMPERATURE SERIES EXPANSIONS FOR SQUARE-LATTICE ISING MODEL WITH FIRST AND SECOND NEIGHBOUR INTERACTIONS

2002 ◽  
Vol 16 (32) ◽  
pp. 4911-4917
Author(s):  
YEE MOU KAO ◽  
MALL CHEN ◽  
KEH YING LIN
Keyword(s):  
Critical Temperature ◽  
Ising Model ◽  
Low Temperature ◽  
Spontaneous Magnetization ◽  
Temperature Series ◽  
Square Lattice ◽  
Series Expansions ◽  
Zero Field ◽  
Ferromagnetic Ising Model ◽  
Neighbour Interaction

We have calculated the low-temperature series expansions of the spontaneous magnetization and the zero-field susceptibility of the square-lattice ferromagnetic Ising model with first-neighbour interaction J1 and second-neighbour interaction J2 to the 30th and 26th order respectively by computer. Our results extend the previous calculations by Lee and Lin to six more orders. We use the Padé approximants to estimate the critical exponents and the critical temperature for different ratios of R = J2/J1. The estimated critical temperature as a function of R agrees with the estimation by Oitmaa from high-temperature series expansions.

scholarly journals Experimental and Numerical Buckling Analyses of Laminated Composite Plates under Temperature Effects

2010 ◽  
Vol 19 (4) ◽  
pp. 096369351001900 ◽  
Author(s):  
Emin Ergun
Keyword(s):  
Composite Plate ◽  
Numerical Solutions ◽  
Laminated Composite ◽  
Composite Plates ◽  
Buckling Load ◽  
Fibre Reinforcement ◽  
Stacking Sequence ◽  
Laminated Composite Plates ◽  
Different Temperatures ◽  
Good Agreement

The aim of this study is to investigate, experimentally and numerically, the change of critical buckling load in composite plates with different ply numbers, orientation angles, stacking sequences and boundary conditions as a function of temperature. Buckling specimens have been removed from the composite plate with glass-fibre reinforcement at [0°]i and [45°]i (i= number of ply). First, the mechanical properties of the composite material were determined at different temperatures, and after that, buckling experiments were done for those temperatures. Then, numerical solutions were obtained by modelling the specimens used in the experiment in the Ansys10 finite elements package software. The experimental and numerical results are in very good agreement with each other. It was found that the values of the buckling load at [0°] on the composite plates are higher than those of other angles. Besides, symmetrical and anti-symmetrical conditions were examined to see the effect of the stacking sequence on buckling and only numerical solutions were obtained. It is seen that the buckling load reaches the highest value when it is symmetrical in the cross-ply stacking sequence and it is anti-symmetrical in the angle-ply stacking sequence.

scholarly journals The bulk, surface and corner free energies of the anisotropic triangular Ising model

2020 ◽  
Vol 476 (2234) ◽  
pp. 20190713
Author(s):  
Rodney J. Baxter
Keyword(s):  
Free Energy ◽  
Ising Model ◽  
Partition Function ◽  
Temperature Series ◽  
Isotropic Case ◽  
Series Expansions ◽  
Exact Results ◽  
Free Energies ◽  
Bulk Surface ◽  
Bulk Free Energy

We consider the anisotropic Ising model on the triangular lattice with finite boundaries, and use Kaufman’s spinor method to calculate low-temperature series expansions for the partition function to high order. From these, we can obtain 108-term series expansions for the bulk, surface and corner free energies. We extrapolate these to all terms and thereby conjecture the exact results for each. Our results agree with the exactly known bulk-free energy and with Cardy and Peschel’s conformal invariance predictions for the dominant behaviour at criticality. For the isotropic case, they also agree with Vernier and Jacobsen’s conjecture for the 60 ° corners.

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