thermodynamics - Is there a phase transition between a gas and plasma?

Does a phase transition occur as a gas is heated to create a plasma? If so, is this a first or second order phase transition?

Also, does the presence of a phase transition depend on the pressure or composition? It seems to me that in the dilute limit (i.e. low pressures), no phase transition should occur because the fraction of atoms that are ionized will follow a Boltzmann distribution, which is a smooth function of temperature. However, the presence of phase transitions in Debye-Hückel theory seems to suggest that a gas-plasma transition could occur at higher pressures.