We show that the self-organized single-helical-axis (SHAx) and double-axis (DAx) states in reversed field pinches can be reproduced in a minimally constrained equilibrium model using only five parameters. This is a significant reduction on previous representations of the SHAx which have required an infinite number of constraints. The DAx state, which has a nontrivial topology, has not previously been reproduced using an equilibrium model that preserves this topological structure. We show that both states are a consequence of transport barrier formation in the plasma core, in agreement with experimental results. We take the limit of zero pressure in this work, although the model is also valid for finite pressure.