Luogo: Aula Maxwell 

Relatore: Guido Giachetti - SISSA and INFN, sezione di Trieste


In the past decades considerable efforts have been made in order to understand the critical features of long-range interacting models, i.e. those where the couplings decay algebraically as r^{-d-\sigma} with \sigma>0, d being the dimension of the system. According to the well-established Sak's criterion for O(N) models, the short-range critical behavior survives up to a given \sigma^{*} \leq 2. However, the applicability of this picture to describe the the two dimensional classical XY model is complicated by  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 first argument, based on Self-Consistent-Harmonic-Approximation, suggests that the BKT transition survives for \sigma < 2. This is confirmed by our more recent field-theoretical analysis. In particular we find there is not a specific, temperature-independent, value of \sigma^{*}: while for \sigma < 7/4 the BKT fixed line vanishes and we have an order-disorder transition, for 7/4 < \sigma < 2 we have the coexistence of a low-temperature broken phase and an intermediate quasi-ordered one. In this regime we were able to fully characterize the critical properties of this new transition.


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