Critical behavior of liquid ⁴He at negative pressures

We examine the equation of state of liquid ⁴He at negative pressures close to the spinodal density ρ_s where the hydrodynamic speed of sound vanishes. The non-analytic behavior of the equation of state and the speed of sound in the vicinity of the spinodal density are calculated in two and in three dimensions; we find for the speed of sound the non-analytic behavior mc_s² ∼ (ρ-ρ_s)^2/5 in three dimensions and mc_s² ∼ [(ρ-ρ_s)/|ln(ρ-ρ_s)|]^1/2 in two dimensions. We then examine the low density regime numerically, using a semi-analytic microscopic theory. It is found that non-analytic exponents are visible only in a negligible density regime around the spinodal point. Estimates for the spinodal densities, and the range of critical fluctuations are provided.