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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.)

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1) The plasma-gas phase transition is a smooth crossover. There are no local order parameters that distinguish the plasma and the gas, and no change of symmetry.

2) In the crossover the ionization fraction changes from 0 to 100% (asymptotically). Other quantities that change are observables that relate to plasma properties, like the Debye radius or the plasma frequency.

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  • $\begingroup$ I'll give you the bounty when it unlocks at midnight UTC time. Please ping me if I forget. $\endgroup$
    – tparker
    Commented Jul 26, 2017 at 7:20
  • $\begingroup$ The ionization fraction does not jump from 0% to 100% unless the ionization process involves some discontinuous energy input (e.g., high energy capacitive discharge). $\endgroup$
    – honeste_vivere
    Commented Jul 26, 2017 at 15:30
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    $\begingroup$ I did not say it "jumps", it's a crossover after all. And 0% and 100% are only asymptotic values, of course. $\endgroup$
    – Thomas
    Commented Jul 26, 2017 at 15:48
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I found the answer to this question at https://physics.stackexchange.com/a/79462/92058. As pointed out here,

the transition from a gas to an ionized gas, i.e., plasma, is not a phase transition, since it occurs gradually with increasing temperature.

So from a Landau symmetry-breaking perspective, gas and plasma are the same phase of matter.

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