Gas-liquid coexistence for the boson square-well fluid and the ${}^4\mathrm{He}$ binodal anomaly

The binodal of a boson square-well fluid is determined as a function of the particle mass through a quantum Gibbs ensemble Monte Carlo algorithm devised by R. Fantoni and S. Moroni [J. Chem. Phys. (to be published)]. In the infinite mass limit we recover the classical result. As the particle mass decreases, the gas-liquid critical point moves at lower temperatures. We explicitly study the case of a quantum delocalization de Boer parameter close to the one of ${}^4\mathrm{He}$. For comparison, we also determine the gas-liquid coexistence curve of ${}^4\mathrm{He}$ for which we are able to observe the binodal anomaly below the $\lambda$-transition temperature.

Figure 1

Linear fit to the zero time-step limit $P\to \infty$ for $T^{*}=1$ and ${\lambda }^{*}=1/100$.

Figure 2

Binodal for the square-well fluid in three dimensions. Shown are the classical results of Vega et al. [10] at ${\lambda }^{*}=0$ and our results in the $P\to \infty$ limit for ${\lambda }^{*}=1/100,1/10$. In the simulations we used $N=50$ and for the extrapolation to the zero time-step limit up to $P=20$ for ${\lambda }^{*}=1/100$ and $P=500$ for ${\lambda }^{*}=1/10$. The curves extrapolating to the critical point are obtained as described in the text. The solid triangles are the expected critical points.

Figure 3

Binodal for the ${}^4\mathrm{He}$ of Aziz [18] in three dimensions. In our simulations we used $N=128$, $r_{\mathrm{cut}}^{*}=6$, and a time step ${\epsilon }^{*}=0.002$. The continuous (red) curve extrapolating to the critical point is obtained as described in the text. The solid triangle is the estimated critical point. The experimental results from Ref. [19] are also shown as a dashed curve.