Critical behavior of liquid He-4 at negative pressures

We examine the equation of state of liquid He-4 at negative pressures close to the spinodal density rho(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(s)(2) similar to (rho - rho(s))(2/5) in three dimensions and mc(s)(2) similar to [(rho - rho(s))/\ln(rho - rho(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.