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 {ital p}/{ital q} is constructed from special values of the integers {ital p} and {ital 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{lt}16 (square lattice) or q{lt}12 (hexagonal lattice). For the other values of {ital p} and {ital q} there can be a spontaneous deformation of the vortex crystal to a commensurable structure if the network potential is sufficiently large. {copyright} {ital 1997} {ital The American Physical Society}