Thermodynamics of a Fermi liquid in a magnetic field

We present calculations of the non-analytic terms in the spin susceptibility chi_s(T) and the specific heat C(T) to systems in a magnetic field. Without a field, chi_s(T) and C(T)/T are linear in T in 2D, while in 3D, chi_s(T) is proportional to T^2 and C(T)/T proportional to T^2 logT. We show that in a magnetic field, the linear in T terms in 2D become scaling functions of mu_B H/T. We present explicit expressions for these functions and show that at high fields, mu_B H >> T, chi_s(T,H) scales as |H|. We also show that in 3D, chi_s(T,H) becomes non-analytic in a field and at high fields scales as H^2 log|H|.