Path-integral Monte Carlo study of low-temperature ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ clusters

Path-integral Monte Carlo calculations have been used to study ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ clusters at low temperatures. We develop a fluctuation formula for the superfluid fraction in terms of a projected area swept out by a path. Manifestations of superfluid behavior are shown to exist in a cluster of 64 atoms and a remnant of the λ transition persists in a cluster of 128 atoms. The temperature dependence of the superfluid fraction is similar to that observed in the liquid.