  Motivated by low energy effective action of string theory and large
applications of BTZ black holes, we will consider minimal coupling between
dilaton and nonlinear electromagnetic fields in three dimensions. The main goal
is studying thermodynamical structure of black holes in this set up.
Temperature and heat capacity of these black holes are investigated and a
picture regarding their phase transitions is given. In addition, the role and
importance of studying the mass of black holes is highlighted. We will see how
different parameters modify thermodynamical quantities, hence thermodynamical
structure of these black holes. In addition, geometrical thermodynamics is used
to investigate thermodynamical properties of these black holes. In this regard,
the successful method is presented and the nature of interaction around bound
and phase transition points is studied.
