A non-paramagnon approach to two-dimensional normal-liquid 3He and the analysis of heat capacity data

Stimulated by recent experiments on the heat capacity of He-3 adsorbed on He-4 precoated Hectorite we shall study the thermodynamics of strongly interacting fermions in two-dimension (2D) at low temperatures. We shall focus on spin fluctuations (SF) and resort to the random phase approximation (RPA) to obtain the thermodynamic potential. To take full account of the degree of freedom of SF, integrals including the RPA susceptibility are calculated numerically over the effectively entire energy-momentum space without imposing the conventional paramagnon approximation or the like. In addition to the T-linear term, we have found that the heat capacity as well as the entropy develop T-2-terms at very low temperatures for T less than or equal to T* and Tlog T-terms which take over the former for T greater than or equal to T*, where T* is the crossover temperature defined numerically. We have compared our results for heat capacity with those obtained experimentally and, as a first finding, located Tlog T-term as predicted. Secondly, in the frame work of Stoner-Hubbard or Landau's Fermi liquid theory, we have proposed and carried out a method of analysis of the data to evaluate the parameters of both theories.