# Is there a phase coexistence line below the critical temperature $T_c$ in normal to superfluid transition?

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?

• 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. – tparker Jul 29 '17 at 5:06

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.
• 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 – SRS Jul 29 '17 at 4:49