New exact solutions, thermodynamics and phase transition in the Einstein–Maxwell-dilaton theory

For the \((n+1)\) $(n+1)$ -dimensional ( \(n\ge 3\) $n\ge 3$ ) dilaton black hole in the Einstein–Maxwell-dilaton theory, we have presented exact analytical solutions of the field equations. These exact solutions include the exact formula of the potential function as well as the exact formula of the metric function. The presence of the dilaton field makes the asymptotic behavior of these black holes no longer flat or anti-de Sitter. We have calculated the electric charge, mass, temperature, entropy and electric potential of these black holes and have shown the correctness of the first law of black hole thermodynamics. As a thermodynamic system, we have analyzed thermal stability of these types of black holes using the canonical ensemble method and, investigated the effect of dilaton field on their stability.