ticles. Our theoretical framework is based on a three-dimensional classical Heisenberg model with nearest magnetic neighbor interactions involving realistic crystalline structure for magnetite with tetrahedral and octahedral irons. Cubic magnetocrystalline anisotropy for core spins, single-ion site anisotropy for surface spins, and interaction with a uniform external magnetic field, were considered. Our results revealed the onset of low temperature exchange bias field at high enough values of the surface anisotropy constant ( KS). Our results indicate also that the strongly pinned spins at high enough surface anisotropy values are responsible for both the horizontal and vertical shifts of the hysteresis loops.