“…The rigorous approach of [42] (see also [43]) uses a multiscale resummation based on conditional expectations and Jensen's inequality. For a recent exposition as well as recent extensions and applications of this approach, see [46,47,55,67], and for recent alternative approaches to the proof of the existence of the Kosterlitz-Thouless transition, see also [2,58,59,66]. These approaches have many appealing features which include that they apply quite robustly to various models, but they are not precise enough to derive scaling limits or sharp asymptotics of correlation functions, or to study the (expected) critical curve -the Kosterlitz-Thouless transition line, see Fig.…”