First- and second-order transitions for a superconducting cylinder in a magnetic field obtained from a self-consistent solution of the Ginzburg-Landau equations

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