Magnetic field induced phase branches of the superconducting transition in one-dimensional π-loop arrays

A description of a field-cooling superconducting phase transition in large-scale one-dimensional pi-loop arrays is given by analysing the free energy of the arrays with a simplified model. The analysis shows that the transition of the arrays splits into two phase branches, the magnetizations with either ferromagnetic or anti-ferromagnetic ordering, which depend periodically on the strength of external magnetic flux phi(e) through each loop and monotonically on the screen parameter beta of the loops in the arrays. The influence of the thermal fluctuation effect on the ordering during the transition from normal to superconducting states of the pi-loop arrays is briefly discussed.