Interplay of spin waves and vortices in the two-dimensional XY model at small vortex-core energy

Maccari, Ilaria; Defenu, Nicoló; Castellani, C.; Enss, Tilman

doi:10.1103/physrevb.102.104505

Cited by 17 publications

(18 citation statements)

References 70 publications

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“…For studies of the KT transition with other truncations of the functional RG, see Refs. [30,[32][33][34][35][36][37][38]. We point out that the present approach, despite the lack of vortices present as explicit degrees of freedom, accurately reproduces the key features of the KT transition, including the phase stiffness jump, the value of η and the essential singularity of the correlation length.…”

Section: Dimensionality D =mentioning

confidence: 59%

Analyticity of critical exponents of the $O(N)$ models from nonperturbative renormalization

Chlebicki

Jakubczyk

2021

SciPost Phys.

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We employ the functional renormalization group framework at the second order in the derivative expansion to study the O(N)O(N) models continuously varying the number of field components NN and the spatial dimensionality dd. We in particular address the Cardy-Hamber prediction concerning nonanalytical behavior of the critical exponents \nuν and \etaη across a line in the (d,N)(d,N) plane, which passes through the point (2,2)(2,2). By direct numerical evaluation of \eta(d,N)η(d,N) and \nu^{-1}(d,N)ν−1(d,N) as well as analysis of the functional fixed-point profiles, we find clear indications of this line in the form of a crossover between two regimes in the (d,N)(d,N) plane, however no evidence of discontinuous or singular first and second derivatives of these functions for d>2d>2. The computed derivatives of \eta(d,N)η(d,N) and \nu^{-1}(d,N)ν−1(d,N) become increasingly large for d\to 2d→2 and N\to 2N→2 and it is only in this limit that \eta(d,N)η(d,N) and \nu^{-1}(d,N)ν−1(d,N) as obtained by us are evidently nonanalytical. By scanning the dependence of the subleading eigenvalue of the RG transformation on NN for d>2d>2 we find no indication of its vanishing as anticipated by the Cardy-Hamber scenario. For dimensionality dd approaching 3 there are no signatures of the Cardy-Hamber line even as a crossover and its existence in the form of a nonanalyticity of the anticipated form is excluded.

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Section: Dimensionality D =mentioning

confidence: 59%

Analyticity of critical exponents of the $O(N)$ models from nonperturbative renormalization

Chlebicki

Jakubczyk

2021

SciPost Phys.

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“…For studies of the KT transition with other truncations of the functional RG, see Refs. [29][30][31][32][33][34][35][36]. We point out that the present approach, despite the lack of vortices present as explicit degrees of freedom, accurately reproduces the key features of the KT transition, including the phase stiffness jump and the essential singularity of the correlation length.…”

Section: Dimensionality D =mentioning

confidence: 62%

Analyticity of critical exponents of the $O(N)$ models from nonperturbative renormalization

Chlebicki,

Jakubczyk

2020

Preprint

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We employ the functional renormalization group framework at second order in the derivative expansion to study the O(N ) models continuously varying the number of field components N and the spatial dimensionality d. We in particular address the Cardy-Hamber prediction concerning nonanalytical behavior of the critical exponents ν and η across a line in the (d, N ) plane, which passes through the point (2, 2). By direct numerical evaluation of η(d, N ) and ν −1 (d, N ) we find no evidence of discontinuous or singular first and second derivatives of these functions for d > 2. The computed derivatives of η(d, N ) and ν −1 (d, N ) become increasingly large for d → 2 and N → 2 and it is only in this limit that η(d, N ) and ν −1 (d, N ) as obtained by us are evidently nonanalytical. We provide a discussion of the evolution of the obtained picture upon varying d and N between (d, N ) = (2, 2) and other, earlier studied cases, such as d → 3 or N → ∞.

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“…A further improvement could be obtained by using estimates of the dielectric constant in the Nelson-Kosterlitz transition, giving k B T BKT = 0.96J 0 [26]. These estimates can be compared with the functional renormalization group estimate, k B T BKT = 0.94J 0 [55], with a (functional) renormalization group calculation using a renormalized initial condition, k B T BKT = 0.89J 0 [56], with the analytic calculation based on the mapping on the 1D quantum XXZ model, k B T BKT = 0.883J 0 [57], and with the previously mentioned Monte Carlo value k B T BKT = 0.893J 0 . We notice that the Nelson-Kosterlitz condition can be used to extract T BKT with high precision from Monte Carlo data [23].…”

Section: Resultsmentioning

confidence: 99%

Self-consistent harmonic approximation with non-local couplings

Giachetti,

Defenu,

Ruffo

et al. 2020

Preprint

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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 ∝ 1/r 2+σ 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 for the lower critical threshold σ * = 2, above which the traditional BKT transition persists in spite of the LR couplings.

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Interplay of spin waves and vortices in the two-dimensional XY model at small vortex-core energy

Cited by 17 publications

References 70 publications

Analyticity of critical exponents of the $O(N)$ models from nonperturbative renormalization

Analyticity of critical exponents of the $O(N)$ models from nonperturbative renormalization

Analyticity of critical exponents of the $O(N)$ models from nonperturbative renormalization

Self-consistent harmonic approximation with non-local couplings

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