Application of the integral operator method for multispin correlation function calculations in the one-dimensional Ising model.

The one-dimensional (1D) Ising model is revisited. The integral operator method is used for the model to derive the general statistical identity for multispin correlation functions. As an application of this identity to generate various correlations, recursive formulas are derived for the correlations of pairs, threes, fours, and fives of spins. Both compact clusters and disjoint sets of spins are considered. It is shown that multispin correlations for the 1D Ising model can be exactly expressed in terms of pairwise correlations using recursive procedures. For clusters with different structures, numerical calculations of multispin correlations as a function of temperature and external magnetic field are performed. The results of these calculations are presented in the figures and discussed.

Mean-field theory of the spin-1/2 transverse field Ising model with a negative thermal expansion.

A generalized spin-1/2 transverse field Ising model with a negative thermal expansion of the lattice is introduced and investigated using standard methods of statistical mechanics. Besides the volume-dependent magnetic energy, the static lattice energy, and anharmonic Einstein phonon energy are also considered in calculations. Analytic relations for the Gibbs free energy, magnetic moments, and equations of state are obtained, taking into account a simple volume dependence of all energy contributions. The ground-state and finite-temperature phase diagrams are discussed in detail for the strong and weak magneto-elastic coupling. It is clearly demonstrated that the generalized spin-1/2 transverse field Ising model exhibits a novel critical behavior, due to the strong negative expansion of the lattice, which is controlled by the strength of magneto-elastic coupling. The presented approach can be easily modified to study also other magnetic and non-magnetic crystalline models of solids.

A novel critical behavior of the spin-1 Blume-Capel model with a distance-dependent nearest-neighbor exchange interaction and magneto-elastic coupling.

A generalized spin-1 Blume-Capel model with distance/volume dependent nearest-neighbor exchange interaction is introduced and investigated using the standard methods of statistical mechanics. Besides of the volume-dependent magnetic energy, the static electromagnetic energy and anharmonic Einstein phonon contribution are also taken into account. Taking the simple volume dependence of all energy contributions we have obtained the equation of state, magnetic moment, internal and Helmholtz free energy of the system. The ground-state and finite-temperature phase diagrams are obtained and discussed in detail. Is it shown that the generalized spin-1 Blume-Capel model exhibits a novel critical behavior appearing due to magnetostriction and thermal volume variations. The presented approach is very universal and easily applicable to many other theoretical models in different fields of solid state physics.

Phase diagram of the J_{1}-J_{2} frustrated anisotropic antiferromagnet with spin S=1 on the quadratic lattice.

In the paper the phase diagram of J_{1}-J_{2} frustrated antiferromagnet with spin S=1 and single-ion anisotropy is studied on the planar quadratic lattice in the cluster approximation. The Bogolyubov inequality is adopted for the Gibbs energy calculation for the case of 2×2 and 4×4 clusters. On this basis, the ranges of existence of the antiferromagnetic, superantiferromagnetic, and paramagnetic phases are investigated for the antiferromagnetic nearest-neighbor (J_{1}<0) and next-nearest-neighbor (J_{2}<0) interactions. In particular, the occurrence of tricritical and triple points is discussed and a comparison between the results for 2×2 and 4×4 clusters is made. The results are also compared with the classical MFA method, adopted here for the model in question, as well as with selected literature results for particular choices of interaction parameters.

Thermodynamic description of the Ising antiferromagnet on a triangular lattice with selective dilution by a modified pair-approximation method.

The pair-approximation method is modified in order to describe systems with geometrical frustration. The Ising antiferromagnet on a triangular lattice with selective dilution (Kaya-Berker model) is considered and a self-consistent thermodynamic description of this model is obtained. For this purpose, the Gibbs free energy as a function of temperature, concentration of magnetic atoms on the selected sublattice, and external magnetic field is derived. In particular, the phase diagram is constructed and a comparison of different methods is presented. The thermodynamic quantities are discussed in the context of their physical validity, and the improvement in the description introduced by the modified method is emphasized.