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The spin-5/2 Blume–Capel model was studied using the mean-field approximation and the Migdal–Kadanoff renormalization group method for two- and three-dimensional systems. We determined the phase diagrams in the (crystal field, temperature) plane where the system exhibited first- and second-order phase transitions as well as isolated critical, bicritical and triple points. In order to show first-order transitions at low temperature, we presented the total magnetization per site and the derivative of the free energy as a function of the crystal field. Moreover, the critical exponents of the system were calculated by linearizing the renormalization transformation at the vicinity of the second-order fixed points. [ABSTRACT FROM AUTHOR]

A ferrimagnetic hexagonal Ising nanotube with spin-1/2 core and spin-5/2 shell is investigated using the mean field approximation (MFA) and the Monte Carlo simulation (MCS). More exactly, we have examined the effects of the exchange interactions and crystal field on the magnetic properties of the system. Our phase diagrams show the appearance of critical and compensation behaviors, as well as first-order phase transitions terminating at isolated critical end-points in the ferrimagnetic phase region at low temperatures. Furthermore, we have made a comparison with other studies of similar nanosystems. [ABSTRACT FROM AUTHOR]