  Being inspired by a recent study [V. Dimitriadis et al. Phys. Rev. B
\textbf{92}, 064420 (2015)], we study the finite temperature magnetic
properties of the spherical nanoparticles with core-shell structure including
quenched (i) surface and (ii) interface nonmagnetic impurities (static holes)
as well as (iii) roughened interface effects. The particle core is composed of
ferromagnetic spins, and it is surrounded by a ferromagnetic shell. By means of
Monte Carlo simulation based on an improved Metropolis algorithm, we implement
the nanoparticles using classical Heisenberg Hamiltonians. Particular attention
has also been devoted to elucidate the effects of the particle size on the
thermal and magnetic phase transition features of these systems. For
nanoparticles with imperfect surface layers, it is found that bigger particles
exhibit lower compensation point which decreases gradually with increasing
amount of vacancies, and vanishes at a critical value. In view of nanoparticles
with diluted interface, our Monte Carlo simulation results suggest that there
exists a region in the disorder spectrum where compensation temperature
linearly decreases with decreasing dilution parameter. For nanoparticles with
roughened interface, it is observed that the degree of roughness does not play
any significant role on the variation of both the compensation point and
critical temperature. However, the low temperature saturation magnetizations of
the core and shell interface regions sensitively depend on the roughness
parameter.
