VIRIAL-THEOREM FOR THE ANISOTROPIC GINZBURG-LANDAU THEORY

The scalar virial theorem for the Ginzburg-Landau theory is generalize d to a vector virial theorem and follows from similar scaling properti es of the Gibbs free-energy density. All the components of the magneti c field H are determined in terms of average values of the kinetic and field tensor components of the Helmholtz free-energy density. We cons ider two frames, the crystal's and the magnetic induction's B, where t he scaling properties yield useful relations due to anisotropy. In the last case the scaling relations do not completely determine H; instea d, they provide useful identities that reflect collective properties o f the vortex state. We compare both the scaling and the thermodynamic methods for the particular case of straight tilted parallel vortex lin es in the London limit.