Self-consistent harmonic approximation with non-local couplings

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 $\propto 1/r^{2+\sigma }$ in order to investigate the robustness, at finite $\sigma$, of the Berezinskii-Kosterlitz-Thouless (BKT) transition, which occurs in the short-range limit $\sigma \to \infty$. 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 for the lower critical threshold ${\sigma }^{\ast }=2$, above which the traditional BKT transition persists in spite of the LR couplings.

Submitted for the special issue "Quantum Long-Range Interactions" in Europhysics Letters, 4 figures

References in corpus (29)

• Statistical mechanics and dynamics of solvable models with long-range interactions
• Quantum Phase Transitions and Vortex Dynamics in Superconducting Networks
• Anharmonic free energies and phonon dispersions from the stochastic self-consistent harmonic approximation: application to platinum and palladium hydrides
• Classical critical behavior of spin models with long-range interactions
• The two dimensional XY model at the transition temperature: A high precision Monte Carlo study
• Continuous symmetry breaking and a new universality class in 1D long-range interacting quantum systems
• A scaling theory for the long-range to short-range crossover and an infrared duality
• The boundary between long-range and short-range critical behavior
• Relations between Short Range and Long Range Ising models
• Long-range critical exponents near the short-range crossover
• Fixed Points Structure & Effective Fractional Dimension for O(N) Models with Long-Range Interactions
• Finite-size scaling method for the Berezinskii-Kosterlitz-Thouless transition
• Large-scale Monte Carlo simulation of two-dimensional classical XY model using multiple GPUs
• The crossover region between long-range and short-range interactions for the critical exponents
• Influence of long-range interactions on the critical behavior of the Ising model
• Long-range Heisenberg models in quasi-periodically driven crystals of trapped ions
• Finite-Size Scaling in Two-Dimensional Superfluids
• Observable Signature of the Berezinskii-Kosterlitz-Thouless Transition in a Planar Lattice of Bose-Einstein Condensates
• Criticality of Spin Systems with Weak Long-Range Interactions
• The Kosterlitz-Thouless Universality Class
• Upper and Lower Critical Decay Exponents of Ising Ferromagnets with Long-range Interaction
• One-dimensional long-range percolation: a numerical study
• Anisotropic Long-Range Spin Systems
• The two-dimensional quantum Heisenberg antiferromagnet: effective Hamiltonian approach to the thermodynamics
• Interplay of spin waves and vortices in the 2D XY model at small vortex-core energy
• Quantum effects on the BKT phase transition of two-dimensional Josephson arrays
• Effects of energy extensivity on the quantum phases of long-range interacting systems
• The low-temperature phase in the two-dimensional long-range diluted XY model
• Finite Temperature Off-Diagonal Long-Range Order for Interacting Bosons

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