scholarly journals Calculation of the Critical Temperature for the Anisotropic Two-Layer Ising Model Using the Transfer Matrix Method

2003 ◽  
Vol 107 (3) ◽  
pp. 829-831 ◽  
Author(s):  
M. Ghaemi ◽  
M. Ghannadi ◽  
B. Mirza
Keyword(s):  
Critical Temperature ◽  
Ising Model ◽  
Transfer Matrix ◽  
Transfer Matrix Method ◽  
Matrix Method

scholarly journals CONSTRUCTING THE CRITICAL CURVE FOR A SYMMETRIC TWO-LAYER ISING MODEL

2004 ◽  
Vol 03 (02) ◽  
pp. 217-224 ◽  
Author(s):  
M. GHAEMI ◽  
B. MIRZA ◽  
G. A. PARSAFAR
Keyword(s):  
Critical Temperature ◽  
Ising Model ◽  
Numerical Method ◽  
Critical Points ◽  
Transfer Matrix Method ◽  
Matrix Method ◽  
Nearest Neighbor ◽  
Neighbor Interaction ◽  
Ising Ferromagnet ◽  
Shift Exponent

A numerical method based on the transfer matrix method is developed to calculate the critical temperature of two-layer Ising ferromagnet with a weak inter-layer coupling. The reduced internal energy per site has been accurately calculated for symmetric ferromagnetic case, with the nearest neighbor coupling K1=K2=K (where K1 and K2 are the nearest neighbor interaction in the first and second layers, respectively) with inter-layer coupling J. The critical temperature as a function of the inter-layer coupling [Formula: see text], is obtained for very weak inter-layer interactions, ξ<0.1. Also a different function is given for the case of the strong inter-layer interactions (ξ>1). The importance of these relations is due to the fact that there is no well tabulated data for the critical points versus J/K. We find the value of the shift exponent ϕ=γ is 1.74 for the system with the same intra-layer interaction and 0.5 for the system with different intra-layer interactions.

scholarly journals Phase transition properties of a finite ferroelectric superlattice from the transverse Ising model.

2000 ◽  
Vol 53 (3) ◽  
pp. 453
Author(s):  
Xiao-Guang Wang ◽  
Ning-Ning Liu ◽  
Shao-Hua Pan ◽  
Guo-Zhen Yang
Keyword(s):  
Phase Transition ◽  
Ising Model ◽  
Curie Temperature ◽  
Transfer Matrix ◽  
Transfer Matrix Method ◽  
Matrix Method ◽  
Type B ◽  
Elementary Unit ◽  
Transverse Ising Model ◽  
Exchange Constants

We consider a finite ferroelectric superlattice in which the elementary unit cell is made up of 1 atomic layers of type A and n atomic layers of type B. Based on the transverse Ising model we examine the phase transition properties of the ferroelectric superlattice. Using the transfer matrix method we derive the equation for the Curie temperature of the superlattice. Numerical results are given for the dependence of the Curie temperature on the thickness and exchange constants of the superlattice.

scholarly journals Ising Model on a Triangular Lattice with Three-spin Interactions. I. The Eigenvalue Equation

1974 ◽  
Vol 27 (3) ◽  
pp. 357 ◽  
Author(s):  
RJ Baxter ◽  
FY Wu
Keyword(s):  
Ising Model ◽  
Transfer Matrix ◽  
Triangular Lattice ◽  
Transfer Matrix Method ◽  
Matrix Method ◽  
Hexagonal Lattice ◽  
Eigenvalue Equation ◽  
Spin Interactions ◽  
A Site

It is shown that the Ising model with three-spin interactions on a triangular lattice is equivalent to a site-colouring problem on a hexagonal lattice. The transfer matrix method is then used to solve the colouring problem. The colouring of two neighbouri

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