Nonlinear Magnetic Response of Superconducting Flux Arrays with Random Pinning

The static nonlinear magnetic response of randomly pinned flux-line lattice in a type-II super-conductor has been investigated using variational replica-symmetry-broken method. A peak in the curve of susceptibility as a function of external magnetic field is found. When the magnetic field is low, there is a softening in the susceptibility as an effect of pinning potential with nonzero correlation length. At some critical magnetic field, the softening changes into hardening. After reaching the maximum in hardening, the susceptibility decreases to its value of piire states with the increase of magnetic field.