"Mixed order phase transitions in one dimension":
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 transition, 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. Examples include models of wetting, glass and jamming transitions, DNA denaturation, rewiring networks and some one-dimensional models with long-range interactions.
An exactly soluble Ising model which provides a link between some of these rather distinct classes of systems is introduced and analyzed through exact calculations and renormalization group (RG) analysis. The RG analysis reveals an intriguing connection between Bose Einstein condensation type transitions and Kosterlitz-Thouless type transitions in one dimension. In addition, the coarsening dynamics of such mixed order transition is presented, and the relation to the voter model and related models is discussed.