Continuous phase transitions, in which the order parameter changes continuously at the transition, exhibit universal features such as critical exponents.  This universality is deeply related to the divergence of a length scale. On the other hand first order transitions, in which the order parameter is discontinuous, are not associated with diverging length scales and hence they are non-universal. This dichotomy fails in quite a number of models which exhibit phase transitions of mixed nature, namely transitions which on the one hand exhibit a diverging correlation length and on the other hand display a discontinuous order parameter. In one dimension such a transition is known to happen in two different classes of models: spin models with inverse distance squared interactions, and models for the pinning depinning transition.

We present a one dimensional exactly soluble Ising model which provides a link between these two rather distinct classes of systems. Its exact and renormalization group (RG) analysis reveals an intriguing connection between Bose Einstein condensation type transitions and Kosterlitz-Thouless type transitions in one dimension.