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 in order to investigate the robustness, at finite σ, of the Berezinskii-Kosterlitz-Thouless (BKT) transition, which occurs in the short-range limit σ → ∞. We propose an ansatz for the functional form of the variational couplings and show that for any σ > 2 the BKT mechanism occurs. The present investigation provides an upper bound σ ∗ = 2 for the critical threshold σ ∗ above which the traditional BKT transition persists in spite of the non-local nature of the couplings.

Self-consistent harmonic approximation in presence of non-local couplings / Giachetti, G.; Defenu, N.; Ruffo, S.; Trombettoni, A.. - In: EUROPHYSICS LETTERS. - ISSN 0295-5075. - 133:5(2021), pp. 1-11. [10.1209/0295-5075/133/57004]

Self-consistent harmonic approximation in presence of non-local couplings

Giachetti, G.;Defenu, N.;Ruffo, S.
;
Trombettoni, A.
2021-01-01

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 in order to investigate the robustness, at finite σ, of the Berezinskii-Kosterlitz-Thouless (BKT) transition, which occurs in the short-range limit σ → ∞. We propose an ansatz for the functional form of the variational couplings and show that for any σ > 2 the BKT mechanism occurs. The present investigation provides an upper bound σ ∗ = 2 for the critical threshold σ ∗ above which the traditional BKT transition persists in spite of the non-local nature of the couplings.
2021
133
5
1
11
57004
10.1209/0295-5075/133/57004
https://iopscience.iop.org/article/10.1209/0295-5075/133/57004/meta
https://arxiv.org/abs/2012.14896
Giachetti, G.; Defenu, N.; Ruffo, S.; Trombettoni, A.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11767/127025
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