Mercoledì 10 Novembre 2021 Ore 16:30 Seminario INFN "Spontaneous Symmetry Breaking versus Berezinskii - Kosterlitz - Thouless scaling in d=2 long-range XY model"

Abstract:

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.