Approximation to the susceptibilities of two-dimensional antiferromagnets

Approximate susceptibilities of square-plane S = ∞ XY and $\text{S =}\text{1}\text{2}$ Ising antiferromagnets are calculated by using the new expansion method reported previously for the case of a square-plane S = ∞ Heisenberg antiferromagnet. The convergence of the new expansion is examined and it is shown that the present method gives a good approximation to the susceptibilities of all of the Heisenberg, XY and Ising antiferromagnets even below the temperature range where the result exhibits a pronounced broad maximum.     

Magnetic specific heat of the honeycomb lattice of spin one-half with anisotropic Heisenberg exchange by a new method

The magnetic specific heat of the honeycomb lattice of $\text{S =}\text{1}\text{2}$ Heisenberg spin with anisotropic exchange is calculated by using the new approximation method reported in a previous paper. In the spin system with the anisotropy parameter |γ|<1 (Ising-Heisenberg system), the specific heat shows a similar divergence as that of the pure Ising spin system, namely a logarithmic divergence at the critical temperature. The same approximation is also applied to the spin system with |γ|>1 (Heisenberg XY system), showing a divergence of the same kind.     

Constant coupling approximation for antiferromagnets with mixed ferro- and antiferromagnetic interactions

The constant-coupling approximation is extended to an antiferromagnetic spin-$\text{1}\text{2}$ system with two distinct anisotropic exchange interactions. The thermodynamic properties such as the transition temperature, magnetization, susceptibility and specific heat are discussed for three special cases: (i) ferro- and antiferromagnetic Ising interactions, (ii) isotropic ferro- and antiferromagnetic Heisenberg interactions; and (iii) isotropic ferromagnetic Heisenberg interactions and antiferromagnetic Ising interactions, allowing in each case for two different nearest-neighbour coupling constants. Numerical calculations have been performed for a layer structure with z = 6 intraplanar and z' = 6 interplanar nearest neighbours and the results are compared with those obtained in other approximations. Applying the theory to FeCl₂, the exchange constants are evaluated. It is shown that the calculated magnitudes of the interactions strongly depend upon the exchange-interaction model assumed.     

Calculation of a pair correlation function for the three-dimensional Ising model with long-range exchange forces

A simple difference equation for one type of correlators has been obtained by the method of direct calculation of the correlation functions (CF). It is correct for the Ising model of an arbitrary dimension with the exactness $\text{O}$($\text{1}\text{z}$) (z-number of particles covered by the interaction potential). The equation obtained is used to calculate the pair CF 〈S^z_fS^z_j〉 in the three-dimensional Ising model with long-range forces which are of importance when dealing with the applied magnetic problems. The results of the calculations lead to corrections in the Ornstein-Zernike (OZ) theory.     

Absence of the second-order phase transitions in the dimerized Ising chains with spin larger than 12

A general spin S Ising chain interacting with a single phonon mode of the harmonic lattice is studied. The thermodynamics of the spin system is calculated exactly for S = 1, $\text{1}\text{2}$ and $\text{3}\text{2}$, while self-consistent equations for the induced lattice distortions are derived. It is demonstrated that for S >$\text{1}\text{2}$ there is no second-order phase transition, in contrast to the case S = $\text{1}\text{2}$ which was proved to have a tricritical point. This is found to cohere with the previous studies of the dimerized magnetic model chains.     

New integral representation for the spin S Ising ferromagnet

A recently discovered integral representation for the spin $\text{1}\text{2}$ Ising ferromagnet is generalized to the case of spin S.     

Critical temperatures of the anisotropic Heisenberg antiferromagnets

The first eight terms of the high temperature series expansions for the mean-square fluctuations of the magnetization variables are derived for the spin $\text{?}\text{1}\text{2}$ anisotropic Heisenberg antiferromagnets. The antiferromagnetic critical temperatures are determined for the s.c. and b.c.c. lattices.     

Two-dimensional decorated Ising model with classical vector spins and Ising spins of magnitude s

A two-dimensional decorated Ising model with ν-dimensional vector spins and Ising spins of magnitude s is considered. The partition function, magnetization and correlation functions are expressed in terms of the average of functions of the spins of the Ising model with effective exchange constants. These results, although derived for a two-dimensional lattice, are valid for a lattice of arbitrary dimensionality. The phase diagram is obtained exactly in the zero external field and two-dimensional lattice for arbitrary values of s and ν, and, as expected, three transition temperatures are obtained for some values of the parameters. It is also shown that for $\text{|}\text{S}\text{|=1, s>}\text{1}\text{2}$ there is an additional ordered phase (up-down/up-down), and for $\text{|}\text{S}\text{|=ν}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ this additional phase can be either up-down/up-down or up-up/down-down depending on the values of ν and s.     

Phase diagram of spin-S Ising model in a random magnetic field

A spin-S Ising model with a random magnetic field is studied in the mean field approximation. It is shown that there is no long-range-order, for any value of S, for the value of the fields $\text{h}\text{SJz}\text{? 0.5}$. Complete phase diagrams are constructed numerically for $\text{S = 1}\text{and}\text{S =}\text{3}\text{2}$.     

Effect of single-ion anisotropy on the critical-point properties of the exchange interaction model of ferromagnetism

For the spin S exchange interaction model it is shown that both magnetic field and single-ion anisotropy (D) can be exactly treated. When D → ± ∞ the critical-point parameters of this model are exactly the same as those of the $\text{S}\text{=}\text{1}\text{2}$ Heisenberg model.     

Specific heat studies of randomly diluted magnets evidence for fractal properties of the infinite percolation cluster

We present specific heat data on the system Fe_pZn_1-pL₆(ClO₄)₂, which is an experimental realization of the sc, $\text{S =}\text{1}\text{2}$, diluted Ising antiferromagnet. Here L = C₅H₅NO. The results are compared with earlier data on the diluted sc, $\text{S =}\text{1}\text{2}$, XY antiferromagnet Co_pZn_1-pL₆(Cl)₄)₂ and the diluted bcc, $\text{S =}\text{1}\text{2}$, Ising antiferromagnet Co_pZn_1-pCs₃Cl₅. The specific heat behaviour of the diluted Ising systems is found to be completely different from that of the diluted XY magnet, for which very strong short-range order effects have been observed. An explanation is given in terms of the fractal properties of the infinite percolation cluster in the temperature range above T_c(p). It is shown that there exists a strong analogy between the specific heat behaviour of a diluted magnet and that of a system of weakly coupled magnetic chains. In this picture a decrease of p corresponds with a decrease of the coupling between the chains. The differences in behaviour observed between the Ising systems on the one hand, and the (isotropic) XY or Heisenberg systems on the other, can then be explained by the fact that the intrachain correlation length depends exponentially on temperature for the Ising chain, whereas it depends much less strongly on temperature (∝ 1/T) for the XY and Heisenberg chains.     

The shape of clusters on rectangular 2D lattices in a simple “phase separation” computer experiment

Phase separation of a binary “50:50 alloy” was simulated in Monte Carlo experiments played on 1D and 2D lattices at T = 0 K using the Ising model framework. $\text{S}$ = total number of bonds/total number of elements, was calculated for the evolving clusters. Surprisingly $\text{S}$/Z (Z = coordination number) is insensitive to the value of Z for Z = 2, 3, 4, 6.     

Ground state of ferromagnet with antiferromagnetic impurity

The Heisenberg ferromagnet with an antiferromagnetic impurity and arbitrary spin is considered. The method is suggested for constructing the ground state of such a system, the method using the Jacobi matrix technique. As an example, there has been investigated the ferromagnet with a simple cubic lattice and the matrix spin $\text{S =}\text{1}\text{2}$, and the impurity spin S′ = 1. The energy and wave function of the ground state are found as dependent on the system parameters.     

Néel temperature of a random binary magnetic system

The Néel temperature of a quenched random system composed of A and B magnetic atoms with negative exchange integrals and $\text{S =}\text{1}\text{2}$ is calculated in the Heisenberg and Ising models, using effective Hamiltonians.     

The parallel magnetic susceptibility and specific heat of the antiferromagnetic Ising linear-chain system with spin S = 2, 52, and 3

The parallel magnetic susceptibility and specific heat of the antiferromagnetic Ising linear-chain system with spin S = 2, $\text{5}\text{2}$, and 3 are calculated using the matrix approach. The results for spin $\text{S =}\text{1}\text{2}$, 1, $\text{3}\text{2}$, and 2 are checked against known results for these cases.     

The effect of the biquadratic exchange interaction on the curie temperature of the mixed ising ferromagnet

For the mixed Ising ferromagnet with S = 1 and $\text{S =}\text{1}\text{2}$, the effect of the biquadratic exchange interaction J′ on the Curie temperature has been calculated by the use of the Bethe-Peierls approximation and its effect is shown to be large for J′ > 0.     

Susceptibility divergence of the spin 1 Ising model on the Cayley tree

The temperature T₂(1), below which the zero-field isothermal susceptibility diverges for the spin 1 Ising model on the M-generation Cayley tree, in the limit as M → ∞, is located. The general approach follows closely that of Falk for the spin $\text{1}\text{2}$ problem. Pruning and retraction identities are used to find upper and lower bounds on the bond-length dependence of the general two-spin correlation function and thence on the susceptibility. A conjecture is advanced regarding the divergence of the higher-order susceptibilities.     

Excitations in the antiferromagnetic Heisenberg chain

Non-singlet excitations of the antiferromagnetic Heisenberg chain of N atoms with spin $\text{1}\text{2}$ are examined. It is found that the energy of the lowest lying excitations for total spin S and wave number q converges to $\text{(}\text{π}\text{2}\text{)|}\text{sin}\text{q |}\text{as}\text{N → ∞,}\text{if only}\text{S?}\text{ln}\text{N}$.     

Linear-chain antiferromagnetism in Ni(N2H5)2(SO4)2

The compound dihydrazinium bis(sulfato) niccolate(II), Ni(N₂H₅)₂(SO₄)₂, containing sulfato-bridged chains of Ni(II) ions, can be described as an antiferromagnetic Heisenberg linear-chain system. A reasonable agreement of susceptibility measurements in the temperature region 2–80K, with a theory developed by Weng for antiferromagnetic Heisenberg linear chains with spin S=1, is obtained for a value of the intra-chain interaction $\text{J}\text{k}\text{=?3.35K}$. Preliminary results of specific heat measurements, on the other hand, do not fit quite well using this model. The origin of this discrepancy is suggested to be a zero-field splitting of the single ion.     

On the properties of the Ising antiferromagnets in the maximum critical field

We demonstrate that all Ising antiferromagnets with general spin S and arbitrary many-neighbour interactions in the maximum critical field have highly degenerate ground states accompanied with nonzero residual entropies. For finite S, the residual entropies vanish when the range of interaction tends to infinity. The proof is realised by establishing bounds for residual entropies in the case of an Ising system situated on a lattice with arbitrary number of dimensions. In addition we estimate the ground-state entropies for a few two-dimensional lattices.