SIMILARITY OF THE LEADING CONTRIBUTIONS TO THE SELF-ENERGY AND THE THERMODYNAMICS IN 2-DIMENSIONAL AND 3-DIMENSIONAL FERMI LIQUIDS

We compare the self-energy and entropy of a two- and three- dimensional Fermi Liquids(FLs) using a model with a contact interaction between fermions. For a two-dimensional(2D) FL we find that there are T2 contributions to the entropy from interactions separate from those due to the collective modes. These T2 contributions arise from non-analytic corrections, to the real part of the self-energy and are analogous to T3lnT contributions present in the entropy of a three-dimensional(3D) FL. The difference between the 2D and 3D results arises solely from the different phase space factors.