In the past decades considerable efforts have been made in orderto understand the critical features of long-range interacting models, i.e. those where the couplings decay algebraically as r^(−d−σ) withσ >0. According to the well-established Sak’s criterion for O(N) models, the short-range critical behavior survives up to a given σ∗≤2. However, the applicability of this picture to describe the the two dimensional classical XY model is complicated by the the presence, in the short-range regime, of a line of RG fixed points,which gives rise to the celebrated Berezinskii – Kosterlitz – Thouless (BKT) phenomenology. Our recent field-theoretical analysis finds there is not a specific, temperature-independent, value of σ∗: while for σ <7/4 the BKT fixed line vanishes and we have an order-disorder transition, for 7/4< σ <2 we have both a low-temperature broken phase and an intermediate quasi-ordered one. In this regime we were able to full characterize the critical properties of this new transition.