High-precision estimate of<i>g</i><sub>4</sub>in the 2D Ising model

Caselle, Michele; Hasenbusch, Martin; Pelissetto, Andrea; Vicari, Ettore

doi:10.1088/0305-4470/33/46/302

Cited by 26 publications

(61 citation statements)

References 15 publications

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“…The calculations demonstrate that the approximants [2/2] and [3/1] constructed for the Borel transform of R 6 do not have dangerous poles, and their processing leads to the values R 6 = 2.970 and R 6 = 2.909, respectively. Averaging these values, we obtain the ratio R 6 = 2.94, which coincides with the results of the calculations performed in [11,16,19,20].…”

Section: Resultssupporting

confidence: 88%

Pseudo-ɛ-Expansion and the Two-Dimensional Ising Model

Sokolov

2005

Phys. Solid State

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-The pseudo-⑀ -expansions for the coordinate of the fixed point g *, the critical exponents, and the sextic effective coupling constant g 6 are determined for the two-dimensional Ising model on the basis of the five-loop renormalization group series. It is found that the pseudo-⑀ -expansions for the coordinate of the fixed point g *, the inverse exponent γ -1 , and the constant g 6 possess a remarkable property, namely, the higher terms of these series are so small that reliable numerical results can be obtained without invoking Borel summation.

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Section: Resultssupporting

confidence: 88%

Pseudo-ɛ-Expansion and the Two-Dimensional Ising Model

Sokolov

2005

Phys. Solid State

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“…Note that, since the Ising fixed point is (0, g * I ), and g * I is known with very high precision from Ref. [79] g * I = 1.7543637 (25),…”

Section: B the Four Loop Seriesmentioning

confidence: 99%

Critical behavior of the two-dimensionalN-component Landau-Ginzburg Hamiltonian with cubic anisotropy

Calabrese

Celi

2002

Phys. Rev. B

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We study the two-dimensional N -component Landau-Ginzburg Hamiltonian with cubic anisotropy. We compute and analyze the fixed-dimension perturbative expansion of the renormalization-group functions to four loops. The relations of these models with N -color Ashkin-Teller models, discrete cubic models, planar model with fourth order anisotropy, and structural phase transition in adsorbed monolayers are discussed. Our results for N = 2 (XY model with cubic anisotropy) are compatible with the existence of a line of fixed points joining the Ising and the O(2) fixed points. Along this line the exponent η has the constant value 1/4, while the exponent ν runs in a continuous and monotonic way from 1 to ∞ (from Ising to O(2)). For N ≥ 3 we find a cubic fixed point in the region u, v ≥ 0, which is marginally stable or unstable according to the sign of the perturbation. For the physical relevant case of N = 3 we find the exponents η = 0.17(8) and ν = 1.3(3) at the cubic transition.

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“…The correct solution of this non-trivial problem was found in remarkable papers belonging to the Italian group of researchers [13,15,16]. The main result is that ω = β (g)| g=gc = 1.75.…”

Section: The Kramers-wannier Symmetrymentioning

confidence: 98%

“…d(d(g)) = g, as it should be. Notice also that the definition of the duality transformation given by equation (15) has a form similiar to the standard KW duality equation, equation (10).…”

Section: The Kramers-wannier Symmetrymentioning

confidence: 99%

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The strong-weak coupling symmetry in 2D Φ^4 field models

Shalaev¹

2005

Condens. Matter Phys.

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It is found that the exact beta-function β(g) of the continuous 2D gΦ 4 model possesses two types of dual symmetries, these being the KramersWannier (KW) duality symmetry and the strong-weak (SW) coupling symmetry f (g), or S-duality. All these transformations are explicitly constructed. The S-duality transformation f (g) is shown to connect domains of weak and strong couplings, i.e. above and below g * . Basically it means that there is a tempting possibility to compute multiloop Feynman diagrams for the β-function using high-temperature lattice expansions. The regular scheme developed is found to be strongly unstable.Approximate values of the renormalized coupling constant g * found from duality symmetry equations are in an agreement with available numerical results.

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High-precision estimate ofg₄in the 2D Ising model

Cited by 26 publications

References 15 publications

Pseudo-ɛ-Expansion and the Two-Dimensional Ising Model

Pseudo-ɛ-Expansion and the Two-Dimensional Ising Model

Critical behavior of the two-dimensionalN-component Landau-Ginzburg Hamiltonian with cubic anisotropy

The strong-weak coupling symmetry in 2D Φ^4 field models

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High-precision estimate ofg4in the 2D Ising model

Cited by 26 publications

References 15 publications

Pseudo-ɛ-Expansion and the Two-Dimensional Ising Model

Pseudo-ɛ-Expansion and the Two-Dimensional Ising Model

Critical behavior of the two-dimensionalN-component Landau-Ginzburg Hamiltonian with cubic anisotropy

The strong-weak coupling symmetry in 2D Φ^4 field models

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Product

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High-precision estimate ofg₄in the 2D Ising model