Transitions of I- and II-order in magnetic field for superconducting cylinder from self-consistent solution of Ginzburg-Landau equations

Basing on self-consistent solution of non-linear GL-equations, the phase boundary is found, which divides the regions of I- and II-order phase transitions of a superconducting cylinder in magnetic field to normal state. This boundary is a complicated function of the parameters (m,R,kappa) (m is the vorticity, R is the cylinder radius, kappa is the GL-parameter), which does not coincide with the simple phase boundary kappa=1/\sqrt{2}, dividing the regions of I- and II-order phase transitions in infinite (open) superconducting systems.