Nonanalytic corrections to the Landau diamagnetic susceptibility in a two-dimensional Fermi liquid

We analyze potential nonanalytic terms in the Landau diamagnetic susceptibility, χdia, at a finite temperature T and/or in-plane magnetic field H in a two-dimensional (2D) Fermi liquid. To do this, we express the diamagnetic susceptibility as χdia=(e/c)2limQ→0Π?JJ(Q)/Q2, where Π?JJ is the transverse component of the static current-current correlator, and evaluate Π?JJ(Q) for a system of fermions with Hubbard interaction to second order in Hubbard U by combining self-energy, Maki-Thompson, and Aslamazov-Larkin diagrams. We find that at T=H=0, the expansion of Π?JJ(Q)/Q2 in U is regular, but at a finite T and/or H, it contains U2T and/or U2|H| terms. Similar terms have been previously found for the paramagnetic Pauli susceptibility. We obtain the full expression for the nonanalytic δχdia(H,T) when both T and H are finite, and we show that the H/T dependence is similar to that for the Pauli susceptibility.