On non-linear magnetic-charged black hole surrounded by quintessence

We derive a non-linear magnetic-charged black hole surrounded by quintessence, which behaves asymptotically like the Schwarzschild black hole surrounded by quintessence but at the short distances like the dS geometry. The horizon properties of this black hole are investigated in detail. The thermodynamics of the black hole is studied in the local and global views. Finally, by calculating the heat capacity and the free energy, we point to that the black hole may undergo a thermal phase transition, between a larger unstable black hole and a smaller stable black hole, at a critical temperature.