My question is a follow-up to Is there a phase transition between a gas and plasma?, with an emphasis on the symmetry-breaking aspect. These questions only refer to electromagnetic plasmas - not quark-gluon plasmas, which are very different.
1) Is the plasma phase transition (in increasing order of "severity") (a) a mere crossover, with no true non-analyticities in any thermodynamic quantities, (b) a second-order transition, or (c) a first-order transition?
2) It it's a crossover, which quantities cross at the transition?
3) If it's a true phase transition, what is the order parameter that changes non-analytically?
4) If it's a second-order transition, what's its universality class?
5) If it's a true phase transition, is it possible to adiabatically connect the gas and plasma states without passing through a phase transition - like it is for the liquid and gaseous states of water - so that from a Landau symmetry-breaking perspective they're actually the same phase?
6) If not, then what symmetry of the Hamiltonian is broken in the gas phase and unbroken in the plasma phase?
(I can't ask these questions in separate posts, because their well-posedness depends on the answers to the previous questions.)