  A theoretical model is developed that can accurately analyze the effects of
thermal fluctuations in antiferromagnetic (AFM) nano-particles. The approach is
based on Fourier series representation of the random effective field with
cut-off frequencies of physical origin at low and high limits while satisfying
the fluctuation-dissipation theorem at the same time. When coupled with the
formalism of a Langevin dynamical equation, it can describe the stochastic
N\'eel vector dynamics with the AFM parameters, circumventing the arbitrariness
of the commonly used treatments in the micro-magnetic simulations. Subsequent
application of the model to spontaneous N\'eel vector switching provides a
thermal stability analysis of the AFM states. The numerical simulation shows
that the AFM states are much less prone to the thermally induced accidental
flips than the ferromagnetic counterparts, suggesting a longer retention time
for the former.
