  In this paper we characterise the equilibrium measure for a nonlocal and
anisotropic weighted energy describing the interaction of positive dislocations
in the plane. We prove that the minimum value of the energy is attained by a
measure supported on the vertical axis and distributed according to the
semi-circle law, a well-known measure which also arises as the minimiser of
purely logarithmic interactions in one dimension. In this way we give a
positive answer to the conjecture that positive dislocations tend to form
vertical walls. This result is one of the few examples where the minimiser of a
nonlocal energy is explicitly computed and the only one in the case of
anisotropic kernels.
