  We obtain an exact spherically symmetric and magnetically charged black hole
solution in 4D Einstein-Gauss-Bonnet gravity coupled with rational nonlinear
electrodynamics. The thermodynamics of our model is studied. We calculate the
Hawking temperature and the heat capacity of the black hole. The phase
transitions occur in the point where the Hawking temperature possesses an
extremum. We show that black holes are thermodynamically stable at some range
of event horizon radii when the heat capacity is positive. The logarithmic
correction to the Bekenstein-Hawking entropy is obtained.

General Physics