Nonlinear electrodynamics and magnetic black holes

A model of nonlinear electrodynamics with two parameters, coupled with general relativity, is investigated. We study the magnetized black hole and obtain solutions. The asymptotic of the metric and mass functions at $r\to \mathrm{\infty }$ and $r\to 0$, and corrections to the Reissner-Nordstr"{o}m solution are found. We investigate thermodynamics of black holes and calculate the Hawking temperature and heat capacity of black holes. It is shown that there are phase transitions and at some parameters of the model black holes are stable.