We studied the compensation behavior, the reentrant phenomena characterizing first order phase transitions, and the exchange bias effect manifested by asymmetric hysteresis loops for a core–shell nanotube with mixed spin (1 , 3 / 2) by combining both the effective field theory and the probability distribution technique. Since our system is intended to be disordered on the shell, a uniform distribution for the exchange anisotropy proposed. Among the interesting results are the compensation behavior in the ideal and disordered cases, where we noticed a critical behavior manifested by total magnetization persistence, the compensation behavior accompanied by the reentrant phenomena, as well as the multi-loops behavior, exchange bias effect, and magnetic susceptibility. Internal energy, Helmholtz free energy, and double peak specific heat are also used to invoke the energetic aspect. • Ferrimagnetic systems' magnetic properties. • Disordered magnetic systems. • Reentrant magnetic phenomena. • Multi-hysteresis loops and hysteresis loops. • First order phase transition and compensation temperature. [ABSTRACT FROM AUTHOR]