Critical behavior of dimensionally continued black holes

The critical behavior of black holes in even and odd dimensional space times is studied based on Ba\~nados-Teitelboim-Zanelli dimensionally continued black holes. In even dimensions it is found that asymptotically flat and anti--de Sitter Reissner-Nordstr\"om black holes present up to two second-order phase transitions. The case of asymptotically anti--de Sitter--Schwarzschild black holes presents only one critical transition and a minimum of temperature, which occurs at the transition. Finally, it is shown that phase transitions are absent in odd dimensions. {} 1996 The American Physical Society.