  A model of nonlinear electrodynamics coupled with the gravitational field is
studied. We obtain the asymptotic black hole solutions at $r\rightarrow 0$ and
$r\rightarrow \infty$. The asymptotic at $r\rightarrow 0$ is shown, and we find
corrections to the Reissner-Nordstr\"om solution and Coulomb's law at
$r\rightarrow\infty$. The mass of the black hole is evaluated having the
electromagnetic origin. We investigate the thermodynamics of charged black
holes and their thermal stability. The critical point corresponding to the
second-order phase transition (where heat capacity diverges) is found. If the
mass of the black hole is greater than the critical mass, the black hole
becomes unstable.
