  In this paper, we investigate the influence of perfect fluid dark matter and
quantum corrections on the thermodynamics of non-linear magnetic-charged black
hole. We consider the metric of the static non-linear magnetic-charged black
hole in the background of perfect fluid dark matter. Starting with the black
hole temperature and the corrected entropy, we use the event horizon propriety
in order to find the temperature, and based on the surface gravity definition,
we find the uncorrected entropy. However, using the definition of the corrected
entropy due to thermal fluctuation, we find and plot the entropy of the black
hole. We find that the entropy is highly affected for smaller non-linear
magnetic-charged black holes. Afterwards, we study the thermodynamic stability
of the black hole by computing and plotting the evolution of heat capacity. The
results show that second-order phase transition occurs, which appears more
later as the dark matter parameter decreases, and leads the black hole to move
from the stable phase to the unstable phase. Furthermore, we show that the heat
capacity for smaller black holes are also affected, since it appears not being
only an increasing function.
