I will present a Hamiltonian mean-field model. The model provides a simplified description of transport in marginally stable systems including vorticity mixing in strong shear flow and electron dynamics in plasmas. Self-consistency is incorporated through a mean-field that couples all the degrees of freedom. The model is formulated as a large set of N coupled standard-like twist maps. Invariant tori and their breakup play a central role in the study of global transport in these self-consistent map examples. I will present an algorithm to compute, continue and approximate the breakdown of analyticity of invariant tori in a simplified version of a self-consistent model. This is joint work with Diego del Castillo, David Martinez and Arturo Olvera.