Thermodynamics of a Fermi liquid in a magnetic field

We extend previous calculations of the nonanalytic 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 two dimensions (2D), while in 3D, chi(s)(T)proportional to T-2 and C(T)/T proportional to T-2 ln T. We show that in a magnetic field, the linear in T terms in 2D become scaling functions of mu H-B/T. We present explicit expressions for these functions and show that at high fields mu H-B > T, chi(s)(T,H) scales as parallel to H parallel to. We also show that in 3D, chi(s)(T,H) becomes nonanalytic in a field and at high fields scales as H-2 ln parallel to H parallel to.