The quantum second virial coefficient of two-dimensional systems interacting with a hard-core or Lennard-Jones 6-12 potential are calculated together with the contribution this coefficient makes to the specific heat of such systems. The results are compared with experimental data from low-density ${\mathrm{He}}^3$ and ${\mathrm{He}}^4$ monolayers adsorbed on graphite. The calculation provides a qualitative and quantitative understandiang of the experimental measurements. In particular it illuminates the manner in which the interaction and the difference in statistics cause the very different specific-heat measurements in the two isotopes. The magnetic susceptibility of low-density ${\mathrm{He}}^3$ monolayers is predicted.

• Received 17 September 1973

DOI:https://doi.org/10.1103/PhysRevA.9.907