Nature of resistive transitions in josephson networks in a magnetic field

We study the depinning of the vortices induced in a Josephson network by a magnetic field. A vortex crystal can be pinned when it can be made commensurate with the network potential by rotation; this can occur only when the number of vortices per unit cell p/q is constructed from special values of the integers p and q. For these cases the transition can be of roughening type; however, melting of the vortex crystal is an important competing process that changes the nature of the transition for q < 16 (square lattice) or q < 12 (hexagonal lattice). For the other values of p and q there can be a spontaneous deformation of the vortex crystal to a commensurable structure if the network potential is sufficiently large.