Random crystal field effects on antiferromagnetic spin-1 Blume–Capel model

The outcome of the random crystal field effects on the antiferromagnetic spin-1 Blume–Capel model and external magnetic field are examined on the Bethe Lattice in terms of exact recursion relations. It is assumed that the crystal field is either turned on or off randomly with probability [Formula: see text] and [Formula: see text], respectively. The phase diagrams are constructed from the thermal analysis of the order parameters with the coordination number [Formula: see text] which corresponds to honeycomb lattice. It is explored that the system goes both second- and first-order phase transitions, along with the reentrant behavior and a few critical points. The reentrant behavior is stronger for lower values of [Formula: see text] and disappears as [Formula: see text] gets closer to 1.0. The first-order lines are observed to be either linked to the tricritical points or decomposed. The critical end points and double critical points are also observed.

Explanation of the cluster structures melting mechanism and their influence on the molten state’s physical and chemical nature

There are results of the melts of semimetals and semiconductors of various structural groups research in the article. On the example of simplified regular Bethe lattice one can model destruction and aggregation of structures in clusters and on it’s basis to substantiate the metal melts properties in the form of nanolayers. The variety of compressibility polytherms forms in electronic melts requires typing, since their analysis makes it possible to explain the mechanism of the aggregation and dissolution processes of extended objects in melts. The article contains formulas that allow explaining the mechanism of the dissolution of cluster structures and their influence on the physicochemical nature of the molten state. There is considered the process of cluster fragmentation. Larger fragments of clusters are formed in the process of crushing, and this fact leads to the compressibility that decreases more rapidly, only after passing through the extremum it begins to increase due to the thermal loosening. The study of the function's compressibility for an extremum in the compressibility's temperature dependence also indicates the changing process of the clusters decomposition mechanisms in melts with an increase in temperature and vice versa to aggregation with a decrease in the melt temperature to the melting temperature.

Trimodal-random field Blume-Capel model

The external random magnetic field [Formula: see text] with three nodes, i.e. acting up and down along the [Formula: see text]-axis and zero, effective on the spins in the Blume-Capel model is analyzed on the Bethe lattice in terms of the exact recursion relations. All the nodes are assumed to have the same probability, [Formula: see text], so that the model could give various kinds of phase transitions. As a mapping of the phase transitions, the phase diagrams are constructed on two different planes which present very rich and interesting phase diagrams. In addition to the second- and first-order phase transitions, a few critical points, reentrant and double reentrant behaviors are also observed.

The thermal properties of the mixed spin-1/2, 1, 3/2 Ising model on the Bethe lattice

A triple mixed-spin Ising system defined on the Bethe lattice is numerically investigated by means of exact recursion relations (ERRs) calculations. The lattice is constituted by three types of magnetic atoms A, B, C with spins [Formula: see text], [Formula: see text], [Formula: see text] respectively arranged in the form ABCABC. The effects of bilinear exchange and crystal-field interactions as well as those of thermal fluctuations on the order parameters and phase diagrams are thoroughly studied and specified. First-order transitions and tricritical points are present for the coordination number [Formula: see text] whereas at [Formula: see text] they are absent. Global compensation phenomena are absent for the magnetic system. Instead, it is shown that it can only occur between the sublattice magnetizations B and C of the system. Several novel kinds of reentrance of the phase boundaries while varying the values of model parameters have been reported.