Phase transition in cylindrical ising nanowires and nanotubes: approximation of the molecular field theory

Within the approximation of the molecular field theory, the critical behavior of cylindrical Ising nanowires and nanotubes is studied. The model considered in this work consists of ferromagnetic spins $S_c$ situated in the core of the system and ferromagnetic spins $S_s$ situated on the surface wall; they are interconnected by the exchange coupling $J_1$. The transition temperature $T_c$ for such systems has been calculated as a function of exchange interaction parameters. The influence of the surface exchange interaction and surface coupling on the magnetodynamic behavior of the system have been studied. Some characteristic properties obtained on the phase diagram are related to the ratio of characteristic physical parameters on the surface and core of the abovementioned nanostructures.