Abstract
We examine the thermodynamics of a two-dimensional Fermi gas model describing adsorbed 3 He in a thin superfluid 4 He film. We show that the magnetic steps seen in experiment are a simple manifestation of the T=0 K equation of state and that the thermal stability of the steps is determined by the larger of Δ ε/2, one-half of the level spacing, and μ m H 0 , the magnetic energy. We derive the conditions under which there exist points in the phase space (termed invariant points) through which all low-temperature isotherms pass exponentially close. The calculated invariant points for the magnetic susceptibility versus coverage are in good agreement with experiment. We calculate the magnetic susceptibility and show that it should exhibit a step-like structure versus 3 He coverage similar to that of the magnetization.
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