  We investigate magnetic fluctuations of a mesoscopic critical region at the
interface induced by smooth time-independent spacial changes of a control
parameter across its critical value. Near the spatial critical point, the order
parameter fluctuations are mesoscopic, i.e., much larger than the lattice
constant but decaying away from the critical region. We propose a minimal model
to describe this behavior and show that it leads to the integrable
Painlev\'e-II equation for the local order parameter. We argue that known
mathematical properties of this equation produce insight into the nonlinear
susceptibilities of this region.
