Thermodynamics of a Fermi liquid in a magnetic field

We extend previous calculations of the nonanalytic terms in the spin susceptibility χₛ(T) and the specific heat $C(T)$ to systems in a magnetic field. Without a field, χₛ(T) and $C(T)∕T$ are linear in T in two dimensions (2D), while in 3D, χₛ(T)∝T² and C(T)∕T∝T²0.2em0exln0.2em0exT. We show that in a magnetic field, the linear in T terms in 2D become scaling functions of μBH∕T. We present explicit expressions for these functions and show that at high fields μBH⪢T, χₛ(T,H) scales as H. We also show that in 3D, χₛ(T,H) becomes nonanalytic in a field and at high fields scales as H²0.2em0exlnH.