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In the present paper, we construct new Gibbs measures for the Ising model on the Cayley tree of order two. Moreover, we find the free energy corresponding to the found measures and compare it with the known ones. [ABSTRACT FROM AUTHOR]

In this paper a computer simulation of phase transitions in epitaxial antiferromagnetic films has been performed. The Ising model and Metropolis algorithm have been used for modeling. The cases of different ratio of exchange interaction constants at the surface and in the film volume are considered. It is shown that in films with no more than six monatomic layers, only the usual phase transition takes place. As the surface energy of spin interaction increases, the temperature of this transition grows. The growth rate of the phase transition temperature decreases as the film thickness increases. If the film thickness is more than six monoatomic layers, a surface phase transition may occur in the system. Antiferromagnetic ordering of spins occurs at temperatures above the Néel point. Phase diagrams of systems with different number of layers are constructed. The tricritical point of the special phase transition has been studied, at this point three lines of the second kind phase transitions intersect. The parameters and temperature of the special transition point for the films of different thickness have been determined. It is shown that the extraordinary transition is a continuous phase transition. The characteristics of the extraordinary phase transition differ from the ordinary second kind phase transition. [ABSTRACT FROM AUTHOR]

In this article, we explore the potential of artificial neural networks, which are trained using an exceptionally simplified catalog of ideal configurations encompassing both order and disorder. We explore the generalization power of these networks to classify phases in complex models that are far from the simplified training context. As a paradigmatic case, we analyze the order–disorder transition of the diluted Ising model on several two-dimensional crystalline lattices, which does not have an exact solution and presents challenges for most of the available analytical and numerical techniques. Quantitative agreement is obtained in the determination of transition temperatures and percolation densities, with comparatively much more expensive methods. These findings highlight the potential of minimalist training in neural networks to describe complex phenomena and have implications beyond condensed matter physics. [Display omitted] • The paper presents a minimalist training catalog for artificial neural networks. • The article proposes using ideal configurations to classify magnetic phases. • Percolation Density in Diluted Ising Models through neural network generalization. [ABSTRACT FROM AUTHOR]

This research paper investigates the electronic structure and magnetic properties of Ti-doped ZnO (Zn 1 − x Ti x O), Cr-doped ZnO (Zn 1 − x Cr x O) and (Ti,Cr)-codoped ZnO (Zn 1 − x Ti x 2 Cr x 2 O) systems with x = 0.08 and 0.12 dopant concentrations using density functional theory (DFT) combined with Monte Carlo simulation (MCS). Ab-initio calculations were based on spin-polarized density functional theory (SDFT) and were carried out within the framework of the GGA+U formalism. The study focuses on the impact of transition metal doping (TM = Ti, Cr) on the structural, electronic, and magnetic properties of the systems. The geometric analysis reveals that lattice parameters and bond lengths between atoms are influenced by the concentration of transition metal (TM) doping. The formation energies of all models indicate their energetic stability, making them suitable for synthesis in the laboratory. The results reveal that Ti-doped ZnO (ZTO), Cr-doped ZnO (ZCO), and (Ti,Cr)-codoped ZnO (ZTCO) systems exhibit a half-metallic behavior, with the Fermi level passing through localized impurity states. These systems behave as n-type semiconductors, with the Fermi level shifting into the conduction band. The presence of transition metal (TM) impurities in ZnO material enhances its magnetic moment and Curie temperature. Additionally, Monte Carlo simulation demonstrates that ZCO exhibits a Curie temperature above room temperature, consistent with experimental studies. Moreover, the co-doping of (Ti,Cr) in ZnO allows for the adjustment of the Curie temperature. At low temperatures, the hysteresis loop becomes more significant. These findings indicate the potential suitability of ZTO, ZCO, and ZTCO systems for spintronic applications. • Ti and Cr doping affect the lattice parameters and bond lengths. • Ti-doped ZnO, Cr-doped ZnO, and (Ti,Cr)-codoped ZnO systems show favorable formation energies for synthesis. • Ti-doped ZnO, Cr-doped ZnO, and (Ti,Cr)-codoped ZnO exhibit half-metallic behavior as n-type semiconductors. • Ti and Cr impurities increase the magnetic moment and Curie temperature of ZnO. • Ti-doped ZnO, Cr-doped ZnO, and (Ti,Cr)-codoped ZnO systems with adjusted Curie temperatures show promise for spintronic applications. [ABSTRACT FROM AUTHOR]