Self-consistent harmonic approximation in presence of non-local couplings. (6th April 2021)

• Record Type: Journal Article
• Authors: Giachetti, Guido; Defenu, Nicolò; Ruffo, Stefano; Trombettoni, Andrea
• Is Part Of: Europhysics letters. Volume 133:Number 5(2021)
• Publication Date: 2021-04-06
• Subjects: 75.30.Kz -- 05.70.Fh; Physics -- Periodicals; Electronic journals; 530.05
• DOI: 10.1209/0295-5075/133/57004
• Languages: English
• ISSNs: 0295-5075

Abstract

Abstract: We derive the self-consistent harmonic approximation for the 2 D XY model with non-local interactions. The resulting equation for the variational couplings holds for any form of the spin-spin coupling as well as for any dimension. Our analysis is then specialized to power-law couplings decaying with the distance r as in order to investigate the robustness, at finite σ, of the Berezinskii-Kosterlitz-Thouless (BKT) transition, which occurs in the short-range limit . We propose an ansatz for the functional form of the variational couplings and show that for any the BKT mechanism occurs. The present investigation provides an upper bound for the critical threshold above which the traditional BKT transition persists in spite of the non-local nature of the couplings.