Self-consistent harmonic approximation in presence of non-local couplings
Year: 2021
Authors: Giachetti G., Defenu N., Ruffo S., Trombettoni A.
Autors Affiliation: SISSA & INFN, Sez Trieste, Via Ronomea 265, I-34136 Trieste, Italy; Swiss Fed Inst Technol, Inst Theoret Phys, Wolfgang Pauli Str 27, CH-8093 Zurich, Switzerland; Univ Trieste, Dept Phys, Str Costiera 11, I-34151 Trieste, Italy; CNR, Ist Sistemi Complessi, Via Madonna Piano 10, I-50019 Sesto Fiorentino, Italy.
Abstract: We derive the self-consistent harmonic approximation for the 2D 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 proportional to 1/r(2+sigma) in order to investigate the robustness, at finite sigma, of the Berezinskii-Kosterlitz-Thouless (BKT) transition, which occurs in the short-range limit sigma -> infinity. 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* = 2 for the critical threshold sigma* above which the traditional BKT transition persists in spite of the non-local nature of the couplings. Copyright (C) 2021 EPLA
Journal/Review: EUROPHYSICS LETTERS
Volume: 133 (5) Pages from: 57004-1 to: 57004-7
More Information: We thank N. Dupuis, T. Enss, G. Gori and I. Nandori for fruitful discussions. We also thank R. Vaia for useful correspondence. This work is supported by the CNR/HAS (Italy-Hungary) project Strongly interacting systems in confined geometries and by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany’s Excellence Strategy EXC-2181/1-390900948 (the Heidelberg STRUCTURES Excellence Cluster). This work is part of MUR-PRIN2017 project Coarse-grained description for non-equilibrium systems and transport phenomena (CONEST) No. 201798CZL whose partial financial support is acknowledged.KeyWords: Long-range Order; Phase-transition; Superfluid Density; Critical-behavior; Dynamics; Systems; ModelDOI: 10.1209/0295-5075/133/57004Citations: 7data from “WEB OF SCIENCE” (of Thomson Reuters) are update at: 2024-10-20References taken from IsiWeb of Knowledge: (subscribers only)