FERROMAGNETIC AND MOTT TRANSITIONS MODULATED BY VARYING FRACTAL DIMENSIONS IN FRACTAL–SHAPED NANOSTRUCTURES

Abstract

The ferromagnetic transition in a fractal-shaped structure is analyzed using standard Monte Carlo simulations of discrete spin models. Mott transition of half-filled electrons in a fractal-shaped structure is investigated using Green's functions for a single-band Hubbard model. Our fractal-shaped structure is generated using the dielectric-breakdown model in a three-dimensional lattice, enabling the fractal dimensions to be reduced from three to two. The critical temperature of the ferromagnetic transition and the critical strength of the electron–electron interaction in the Mott transition are dependent on the fractal dimensions, thus the critical values of these phase transitions can be modulated by varying fractal dimensions.