  We consider a two leg bosonic ladder in a $U(1)$ gauge field with both
interleg hopping and interleg repulsion. As a function of the flux, the
interleg interaction converts the commensurate-incommensurate transition from
the Meissner to a Vortex phase, into an Ising-type of transition towards a
density wave phase. A disorder point is also found after which the correlation
functions develop a damped sinusoid behavior signaling a melting of the vortex
phase. We discuss the differences on the phase diagram for attractive and
repulsive interleg interaction. In particular, we show how repulsion favors the
Meissner phase at low-flux and a phase with a second incommensuration in the
correlation functions for intermediate flux, leading to a richer phase diagram
than in the case of interleg attraction. The effect of the temperature on the
chiral current is also discussed.
