Selfconsistent harmonic approximation in presence of nonlocal couplings
Abstract
We derive the selfconsistent harmonic approximation for the 2D XY model with nonlocal interactions. The resulting equation for the variational couplings holds for any form of the spinspin coupling as well as for any dimension. Our analysis is then specialized to powerlaw couplings decaying with the distance r as $\propto 1/r^{2+\sigma}$ in order to investigate the robustness, at finite σ, of the BerezinskiiKosterlitzThouless (BKT) transition, which occurs in the shortrange limit $\sigma \to \infty$ . We propose an ansatz for the functional form of the variational couplings and show that for any $\sigma>2$ ?> the BKT mechanism occurs. The present investigation provides an upper bound $\sigma^\ast=2$ for the critical threshold $\sigma^\ast$ above which the traditional BKT transition persists in spite of the nonlocal nature of the couplings.
 Publication:

EPL (Europhysics Letters)
 Pub Date:
 March 2021
 DOI:
 10.1209/02955075/133/57004
 arXiv:
 arXiv:2012.14896
 Bibcode:
 2021EL....13357004G
 Keywords:

 75.30.Kz;
 05.70.Fh;
 Condensed Matter  Statistical Mechanics
 EPrint:
 Submitted for the special issue "Quantum LongRange Interactions" in Europhysics Letters, 4 figures