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

Corrected thermodynamics of non-linear magnetic-charged black hole surrounded by perfect fluid dark matter