Borel resummation of the ɛ-expansion of the dynamical exponent z in model a of the ϕ 4(O(n)) theory

Nalimov, M. Yu.; Сергеев, В. А.; Sladkoff, L

doi:10.1007/s11232-009-0040-4

Cited by 23 publications

(12 citation statements)

References 23 publications

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“…To make results more reliable one needs to incorporate into the reconstructed series all the information we know about it [13]. For example, for the ϕ 4 model (and some other models) we know high order asymptotics (HOA) for A n [8]:…”

Section: General Considerationsmentioning

confidence: 99%

Prediction of the higher-order terms based on Borel resummation with conformal mapping

Kompaniets

2016

J. Phys.: Conf. Ser.

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Section: General Considerationsmentioning

confidence: 99%

Prediction of the higher-order terms based on Borel resummation with conformal mapping

Kompaniets

2016

J. Phys.: Conf. Ser.

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“…For the critical dynamical exponent of the 2D φ 4 -model, z ≈ 2 was mentioned in Ref. [16], and the -expansion method has shown that z c ∈ (2.04, 2.14) [17]. Further, z c has been measured using the heat bath algorithm, yielding z c = 1.9 ± 0.21 [18].…”

Section: Introductionmentioning

confidence: 97%

Critical dynamical exponent of the two-dimensional scalar ϕ4 model with local moves

et al. 2018

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We study the scalar one-component two-dimensional (2D) φ 4 -model by computer simulations, with local Metropolis moves. The equilibrium exponents of this model are well-established, e.g. for the 2D φ 4 -model γ = 1.75 and ν = 1. The model has also been conjectured to belong to the Ising universality class. However, the value of the critical dynamical exponent z c is not settled. In this paper, we obtain z c for the 2D φ 4 -model using two independent methods: (a) by calculating the relative terminal exponential decay time τ for the correlation function Φ(t)Φ(0) , and thereafter fitting the data as τ ∼ L zc , where L is the system size, and (b) by measuring the anomalous diffusion exponent for the order parameter, viz., the mean-square displacement (MSD) ∆Φ 2 (t) ∼ t c as c = γ/(νz c ), and from the numerically obtained value c ≈ 0.80, we calculate z c . For different values of the coupling constant λ, we report that z c = 2.17 ± 0.03 and z c = 2.19 ± 0.03 for the two methods respectively. Our results indicate that z c is independent of λ, and is likely identical to that for the 2D Ising model. Additionally, we demonstrate that the Generalized Langevin Equation (GLE) formulation with a memory kernel, identical to those applicable for the Ising model and polymeric systems, consistently captures the observed anomalous diffusion behaviour.

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“…This makes it useless for problems in QFT [4,10] or many-body perturbation theory in condensed matter physics [14] where ≲10 orders are available at best. In such cases the Borel-Padé (BP) technique can be used together with a conformal transformation in the Borel plane [1,10,[30][31][32][33][34][35][36][37]]. …”

Section: Introductionmentioning

confidence: 99%

Fast summation of divergent series and resurgent transseries from Meijer- G approximants

2018

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We develop a resummation approach based on Meijer-G functions and apply it to approximate the Borel sum of divergent series and the Borel-Écalle sum of resurgent transseries in quantum mechanics and quantum field theory (QFT). The proposed method is shown to vastly outperform the conventional Borel-Padé and Borel-Padé-Écalle summation methods. The resulting Meijer-G approximants are easily parametrized by means of a hypergeometric ansatz and can be thought of as a generalization to arbitrary order of the Borel-hypergeometric method [Mera et al., Phys. Rev. Lett. 115, 143001 (2015)]. Here we demonstrate the accuracy of this technique in various examples from quantum mechanics and QFT, traditionally employed as benchmark models for resummation, such as zero-dimensional ϕ 4 theory; the quartic anharmonic oscillator; the calculation of critical exponents for the N-vector model; ϕ 4 with degenerate minima; self-interacting QFT in zero dimensions; and the summation of one-and two-instanton contributions in the quantum-mechanical double-well problem.

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Borel resummation of the ɛ-expansion of the dynamical exponent z in model a of the ϕ 4(O(n)) theory

Cited by 23 publications

References 23 publications

Prediction of the higher-order terms based on Borel resummation with conformal mapping

Prediction of the higher-order terms based on Borel resummation with conformal mapping

Critical dynamical exponent of the two-dimensional scalar ϕ4 model with local moves

Fast summation of divergent series and resurgent transseries from Meijer- G approximants

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