Magnetic Properties of the Random Mixture of the Classical Heisenberg Spins

1975 ◽  
Vol 53 (9) ◽  
pp. 854-860 ◽  
Author(s):  
Shigetoshi Katsura
Keyword(s):  
Critical Temperature ◽  
Nearest Neighbor ◽  
Linear Chain ◽  
Three Dimensional ◽  
Bethe Lattice ◽  
Zero Field ◽  
Qualitative Properties ◽  
Neighbor Interaction ◽  
Random Mixture ◽  
Ising Spins

The specific heat, the susceptibility, and the correlation function at zero field above the critical temperature of the random mixture (quenched site and bond problems) of the classical Heisenberg spins with nearest neighbor interaction were obtained exactly for the linear chain and for an infinite Bethe lattice (Bethe approximation of the two and three dimensional lattices) above the critical temperature. The results are simply expressed by the replacements of 2 cosh K → 4π (sinh K)/K and tanh K → L(K) (L(K) = Langevin function) for K = KAA, KAB, KBA, and KBB in the corresponding expressions of the random mixture of the Ising spins, and qualitative properties of both models are similar.

Magnetic Properties of the Random Mixture of Ising Spins

1974 ◽  
Vol 52 (2) ◽  
pp. 120-130 ◽  
Author(s):  
Shigetoshi Katsura ◽  
Fumitaka Matsubara
Keyword(s):  
Magnetic Properties ◽  
Binary Mixture ◽  
Three Dimensional ◽  
Bethe Lattice ◽  
Experimental Result ◽  
Specific Heats ◽  
Random Mixture ◽  
The One ◽  
Critical Lines ◽  
Ising Spins

A method of obtaining the magnetic properties of the random mixture of plural kinds of magnetic atoms (including nonmagnetic atoms) in both the site and the bond problems is presented. The specific heats and the susceptibilities of the one-dimensional binary mixture and the binary Bethe lattice are exactly given. The phase transitions of both the Bethe lattice and the ordinary two- and three-dimensional lattices are also discussed. It is shown that the phase boundary of an ordinary binary mixture in the site problem is rather similar to that in the bond problem when JAAJBB > 0 and JαJβ > 0, while they are quite different when JAAJBB < 0 and JαJβ < 0. In the latter case, the two critical lines of ordinary lattice, on which the uniform or the staggered susceptibility diverges, cross at some value of concentration of magnetic atoms, while they are separated by the paramagnetic phase in the bond problem. The experimental result for (MnxCr1−x)Sb is similar to the former and that for Co(SxSe1−x)2 is similar to the latter.

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.

On Next‐Nearest‐Neighbor Interaction in Linear Chain. II

1969 ◽  
Vol 10 (8) ◽  
pp. 1399-1402 ◽  
Author(s):  
Chanchal K. Majumdar ◽  
Dipan K. Ghosh
Keyword(s):  
Nearest Neighbor ◽  
Linear Chain ◽  
Neighbor Interaction

On Next‐Nearest‐Neighbor Interaction in Linear Chain. I

1969 ◽  
Vol 10 (8) ◽  
pp. 1388-1398 ◽  
Author(s):  
Chanchal K. Majumdar ◽  
Dipan K. Ghosh
Keyword(s):  
Nearest Neighbor ◽  
Linear Chain ◽  
Neighbor Interaction

DYNAMICS ON MULTILAYERED HYPERBRANCHED FRACTALS THROUGH CONTINUOUS TIME RANDOM WALKS

2012 ◽  
Vol 26 (09) ◽  
pp. 1250055 ◽  
Author(s):  
ANTONIO VOLTA ◽  
MIRCEA GALICEANU ◽  
AUREL JURJIU ◽  
TOMMASO GALLO ◽  
LUCIANO GUALANDRI
Keyword(s):  
Nearest Neighbor ◽  
Linear Chain ◽  
Three Dimensional ◽  
Connectivity Matrix ◽  
Eigenvalue Spectrum ◽  
Large Structures ◽  
Long Time ◽  
Continuous Time Random Walks ◽  
Intermediate Time ◽  
Short Time

We introduce a new method to generate three-dimensional structures, with mixed topologies. We focus on Multilayered Regular Hyperbranched Fractals (MRHF), three-dimensional networks constructed as a set of identical generalized Vicsek fractals, known as Regular Hyperbranched Fractals (RHF), layered on top of each other. Every node of any layer is directly connected only to copies of itself from nearest-neighbor layers. We found out that also for MRHF the eigenvalue spectrum of the connectivity matrix is determined through a semi-analytical method, which gives the opportunity to analyze very large structures. This fact allows us to study in detail the crossover effects of two basic topologies: linear, corresponding to the way we connect the layers and fractal due to the layers' topology. From the wealth of applications which depends on the eigenvalue spectrum we choose the return-to-the-origin probability. The results show the expected short-time and long-time behaviors. In the intermediate time domain we obtained two different power-law exponents: the first one is given by the combination linear-RHF, while the second one is peculiar either of a single RHF or of a single linear chain.

Computer simulation of phase transitions of the Heisenberg antiferromagnetic model

2019 ◽  
pp. 25-31
Author(s):  
M.K. Ramazanov ◽  
A.K. Murtazaev
Keyword(s):  
Computer Simulation ◽  
Phase Transitions ◽  
Nearest Neighbor ◽  
Three Dimensional ◽  
Exchange Interactions ◽  
Nearest Neighbors ◽  
Neighbor Interaction ◽  
A Value ◽  
The Monte Carlo Method ◽  
Antiferromagnetic Model

Based on the replica algorithm by the Monte Carlo method, a computer simulation of the three-dimensional antiferromagnetic Heisenberg model is performed, taking into account the interactions of the first and second nearest neighbors. The phase transitions of this model are studied. The investigations were carried out for the ratios of the exchange interactions of the first and second nearest neighbors $r = J_2 / J_1$ in the range $0.0 \leq r \leq 1.0$. The phase diagram of the critical temperature dependence on a value of the next-nearest neighbor interaction is plotted.

Effect of the Local Disorder in a-Si on the Electronic Density of States at the Band Edges.

1991 ◽  
Vol 219 ◽  
Author(s):  
B. N. Davidson ◽  
G. Lucovsky ◽  
J. Bernholc
Keyword(s):  
Density Of States ◽  
Nearest Neighbor ◽  
Bond Angle ◽  
Local Density ◽  
Tight Binding ◽  
Bethe Lattice ◽  
Neighbor Interaction ◽  
Lattice Method ◽  
Electronic Density ◽  
Interaction Terms

ABSTRACTWe have systematically investigated the formation of electronic states in the region of the conduction and valence band edges of a Si as functions of variations in the bond angle distributions. Local Density of States (LDOS) for Si atoms in disordered environments have been calculated using the cluster Bethe lattice method with a tight-binding Hamiltonian containing both first and second nearest neighbor interaction terms. LDOS for atoms with bond angle dis ortions in the nearest neighbor and second neighbor shells are compared and contrasted, both showing an influence on the LDOS near the gap. We also consider the role of the second neighbor term in the Hamiltonian by comparing the DOS for a distoned infinite Bethe lattice using Hamiltonians with and without the second neighbor interactions. It is found that in this case the second neighbor interaction terms cause greater conduction band tailing than using the nearest neighbor interaction terms alone.

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