Thermodynamic Behavior of Type-II Superconductors with Smallκnear the Lower Critical Field

The interaction between well-separated Abrikosov vortices is calculated with the Ginzburg-Landau theory for superconductors with $\kappa <\sqrt{2}$. For $\kappa >\frac{1}{\sqrt{2}}$, vortices repel each other while for $\kappa <\frac{1}{\sqrt{2}}$ there is an attraction. Therefore, in the Ginzburg-Landau regime, all type-II superconductors exhibit a $\lambda$ transition gradually changing into a first-order transition as $\kappa \to \frac{1}{\sqrt{2}}$. Slightly above $H_{c1\mathrm{}}$ a transition from the triangular- to the square-flux-line lattice is found to take place. The variational method used admits more general applications.