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The coordination numbers z = 3, 4 and 6 corresponding to the honeycomb, square, and simple cubic lattices, respectively, are randomly taken with probabilities p; q; r between the nearest-neighbors of spin-1 atoms on the Bethe lattice to simulate amorphous materials. The exact recursion relations are employed to obtain the orderparameters with the implementation of random coordination numbers in the standard-random approach. The phase diagrams are obtained by varying the temperature for given values of crystal field, coordination numbers, and probabilities. It is found that the phase lines consist of either second- or first-order phase transitions and secondand first-order phase transitions combined at the tricritical points for appropriate values of our parameters. [ABSTRACT FROM AUTHOR]

The square-type nanowire is simulated on the Bethe lattice by using the core-shell structure consisting of the Ising spins. A nanoparticle is formed by placing a spin to the center and four others to the corners of a square. Then, each nanoparticle is combined with two neighboring ones with a perfect alignment of the squares to form the nanowire. Only nearest-neighbor spin interactions, either ferromagnetic or antiferromagnetic type, are allowed. The phase diagrams are calculated by studying the thermal variations of magnetizations for various values of bilinear interactions. It is found that the model gives both second- and first-order phase transitions in addition to the tricritical points and compensation temperatures. [ABSTRACT FROM AUTHOR]