Fluxoids configurations in finite superconducting networks

Analysis of superconducting ladders consisting of rectangular loops, yields an Ising like expression for the total energy of the ladders as a function of the loops vorticities and the applied magnetic field. This expression shows that fluxoids can be treated as repulsively interacting objects driven towards the ladder center by the applied field. Distinctive repulsive interactions between fluxoids are obtained depending on the ratio l between the loops length and the common width of adjacent loops. A 'short range' and a 'long range' interactions obtained for l ≳ 1 and l ≪ 1, respectively, give rise to remarkably different fluxoid configurations. The different configurations of fluxoids in different types of ladders are illustrated by simulations.