  The nonequilibrium behaviour of a core-shell nanoparticle has been studied by
Monte- Carlo simulation. The core consists of Ising spins of $\sigma=1/2$ and
the shell contains Ising spins of $S=1$. The interactions within the core and
in the shell are considered ferromagnetic but the interfacial interaction
between core and shell is antiferromagnetic. The nanoparticle system is kept in
open boundary conditions and is driven by randomly varying (in time but uniform
over the space) magnetic field. Depending on the width of the randomly varying
field and the temperature of the system, the core, shell and total
magnetization varies in such a manner that the time averages vanish for higher
magnitude of the width of random field, exhibiting a dynamical symmetry
breaking transitions. The susceptibilities get peaked at two different
temperatures indicating nonequilibrium multiple transitions. The phase
boundaries of the nonequilibrium multiple transitions are drawn in the plane
formed by the axes of temperature and the width of the randomly varying field.
Furthermore, the effects of the core and shell thicknesses on the multiple
transitions have been discussed.
