Nature of Phase Transitions of Superconducting Wire Networks in a Magnetic Field

We study $I-V$ characteristics of periodic square Nb wire networks as a function of temperature in a transverse magnetic field, with a focus on three fillings 2/5, 1/2, and 0.618 that represent very different levels of incommensurability. For all three fillings, a scaling behavior of $I-V$ characteristics is found, suggesting a finite temperature continuous superconducting phase transition. The low-temperature $I-V$ characteristics are found to have an exponential form, indicative of the domain-wall excitations.