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In the case of water, there is a phase coexistence line (called the liquid-gas coexistence curve) which ends in a critical point. And this line separates the gas phase from the liquid phase in the P-T phase diagram.

1. Do we observe such coexistence line below $T_c$ in the case of normal to superfluid transition below the critical point?

2. If yes, what are the phases that this line separates?

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  • $\begingroup$ Could you sketch the phase diagram that you're visualizing? I understand what you mean by "phase coexistence," but I don't understand the "phase coexistence line" that you're considering. $\endgroup$ – tparker Jul 29 '17 at 5:06
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A phase coexistence line is a first-order transition. I believe that the superfluid transition is always second-order, so there is no phase coexistence line.

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  • $\begingroup$ Dear @tparker Would you like to comment as to why this is the case? $\endgroup$ – SRS Aug 1 '17 at 10:50
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The liquid and the gas have the same symmetries, so the phase transition line can end in a critical point. The fluid and the superfluid do not have the same symmetries (the superfluid has a broken $U(1)$ symmetry), so the phase transition line cannot end.

The simplest possibility is that at any pressure the superfluid transition is at lower temperature than the liquid-gas transition. In this case there are two different lines, which never meet. Below the critical pressure of the liquid-gas endpoint you encounter two transitions when you cool the gas. The first is liquification, the second is superfluidity. Above $P(crit)$ there is only one transition, which is the superfluid transition. The phase diagram of liquid helium does indeed look like this.

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  • $\begingroup$ The coexistence is between liquid-gas. Not between liquid-fluid or gas-fluid where by fluid I mean the phase above $T_c$. I'm asking what happens below $T_c$. Below $T_c$ there is normal fluid and the question of normal fluid coexisting with superfluid doesn't make sense. @Thomas $\endgroup$ – SRS Jul 29 '17 at 4:49
  • $\begingroup$ @SRS Sorry, I misread your question. I edited the answer. $\endgroup$ – Thomas Aug 2 '17 at 21:55

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