A study of the fractal characteristics of the Ising model with a random magnetic field on the Bethe lattice

The fractal characteristics of a set of the effective field values are calculated for the Ising model with a random local magnetic field on the Bethe lattice. The dependence of these characteristics on the random field value is investigated. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 12, pp. 14–18, December, 2005.     

A Quantum Particle in a One-Dimensional Fractal Field

Algorithms have been obtained for calculating reflection coefficients for a particle incident on a fractal potential barrier or on a fractal potential well. It has been investigated how these coefficients vary with the energy of the particle and with the fractal dimension and other parameters of the barrier or well. The energies of the bound states of fractal potential wells have been calculated.