Thermodynamic stability of BTZ dilaton black holes

We study thermodynamic stability of static Banados-Teitelboim-Zanelli (BTZ) black hole solutions in the framework of dilaton gravity and investigate the effects of the dilaton field on the stability of the solutions. We find that these solutions can represent a dilaton BTZ black hole with a horizon provided the dilaton parameter satisfies alpha <= 1. We obtain the temperature and the entropy of the solutions. Using the counterterm method, we calculate the quasilocal mass and check the first law of black hole thermodynamics. Finally, we analyze the thermodynamic stability in the canonical ensemble and show that the system is thermally stable for alpha < 1/root 2, while for alpha > 1/root 2 the system has an unstable phase.