Properties of the ideal Ginzburg-Landau vortex lattice

The magnetization curves $M\left(H\right)\mathrm{}$ for ideal type-II superconductors and the maximum, minimum, and saddle-point magnetic fields of the vortex lattice are calculated from Ginzburg-Landau theory for the entire ranges of applied magnetic fields $H_{c1\mathrm{}}<~H<~H_{c2\mathrm{}}$ or induction $0<~B<~{\mu }_0{H}_{c2\mathrm{}}$ and Ginzburg-Landau parameters $2^{-1/2}<~\kappa <~1000.$ Results for the triangular and square flux-line lattices are compared with the results of the circular cell approximation. The exact magnetic field $B(x,y)\mathrm{}$ and magnetization $M(H,\kappa )$ are compared with often used approximate expressions, some of which deviate considerably or have limited validity. Useful limiting expressions and analytical interpolation formulas are presented.