Pauli paramagnetic gas in the framework of Riemannian geometry

We investigate the thermodynamic curvature resulting from a Riemannian geom etry approach to thermodynamics for the Pauli paramagnetic gas which is a s ystem of identical fermions each with spin 1/2, and also for classical idea l paramagnetic gas. We find that both the curvature of classical ideal para magnetic gas and the curvature of the Pauli gas in the classical limit redu ce to that of a two-component ideal gas. On the other hand, it is seen stra ightforwardly that the curvature of classical gas satisfies the geometrical equation exactly. Also a simple relationship between the curvature of Paul i gas and the correlation volume is obtained. We see that it is only in the classical and semiclassical regime that the absolute value of the thermody namic curvature can be interpreted as a measure of the stability of the sys tem. [S1063-651X(99)09009-1].