Mixed order phase transitions: from DNA denaturation to jamming processes

Phase transitions of mixed nature, which on the one hand exhibit a diverging correlation length as in second order transitions and on the other hand display a discontinuous order parameter as in first order transitions have been observed in a diverse classes of physical systems. Examples include DNA denaturation, models of wetting, glass and jamming transitions, 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. Renormalization group analysis which provides a common framework for studying some of these systems, elucidating the relation between them will be discussed as well as the extreme value statistics of the locally ordered domains that characterize the various phases.