ABSTRACT
Following the distinction in §2.1 between extensive and intensive variables, we note that for magnetic systems the extensive variable is the magnetization, M, and the intensive variable is the magnetic field, H. In order to find the appropriate analogue of equation (2.3), an analysis must be undertaken of the external work done in a magnetization process. The problem is tackled from first principles by Pippard (1957, pp. 24-6), who demonstrates conclusively that the correct analogue is
when the magnetization M and field H are not in the same direction, and
in the more usual case when the magnetization and field are in the same direction. The fundamental relation corresponding to (2.7) is then
The first Legendre transformation changes the extensive variable S into the intensive variable T; it has become common practice to denote the corresponding free energy by A(T,M):
The second Legendre transformation changes the extensive variable M into the intensive variable H. For reasons related to the canonical ensemble in
statistical mechanics, which we will discuss shortly, the corresponding free energy is denoted by F(T,H):
Thus, F(T,H) for magnets is the analogue of G(T,P) for fluids; this is quite confusing, but the notation has become so widespread that it is difficult to advocate any change.
