  We study the thermodynamics of Ayon Beato-Garcia black hole and the relation
between the photon orbits and the thermodynamic phase transition of the black
hole. Then we study the interaction between the microstructures of the black
hole using Ruppeiner geometry. The radius of photon orbit and minimum impact
parameter behave non-monotonously below the critical point, which mimics the
behaviour of Hawking temperature and pressure in extended thermodynamics. Their
change during the large black hole and small black hole phase transition serve
as the order parameter, having a critical exponent $1/2$. The results show that
gravity and thermodynamics of Ayon Beato-Garcia black hole are closely related.
Following this we study the thermodynamic geometry which gives insight of the
microstructure interaction of the black hole. We find that the large black hole
phase is analogous to bosonic gas with a dominant attractive interaction, and
the small black hole phase behaves like an anyonic gas with both attractive and
repulsive interactions.
