Scale-free Monte Carlo method for calculating the critical exponent<i>γ</i>of self-avoiding walks

Clisby, Nathan

doi:10.1088/1751-8121/aa7231

Cited by 53 publications

(83 citation statements)

References 30 publications

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“…The DE of the NPRG equations has proved to be an approximation scheme which is versatile and capable of [75], MC [76,77], Length doubling method series [78], and 6-loop, d = 3 perturbative RG values [2], and −expansion at order 5 [2] and order 6 [48] are also given for comparison. Results for most precise experiment are also included (polystyrene benzene dilute solutions [74].…”

Section: Discussionmentioning

confidence: 99%

Precision calculation of critical exponents in the O(N) universality classes with the nonperturbative renormalization group

et al. 2020

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We compute the critical exponents ν, η and ω of O(N ) models for various values of N by implementing the derivative expansion of the nonperturbative renormalization group up to next-to-nextto-leading order [usually denoted O(∂ 4 )]. We analyze the behavior of this approximation scheme at successive orders and observe an apparent convergence with a small parameter -typically between 1/9 and 1/4 -compatible with previous studies in the Ising case. This allows us to give well-grounded error bars. We obtain a determination of critical exponents with a precision which is similar or better than those obtained by most field theoretical techniques. We also reach a better precision than Monte-Carlo simulations in some physically relevant situations. In the O(2) case, where there is a longstanding controversy between Monte-Carlo estimates and experiments for the specific heat exponent α, our results are compatible with those of Monte-Carlo but clearly exclude experimental values. arXiv:2001.07525v1 [cond-mat.stat-mech]

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Section: Discussionmentioning

confidence: 99%

Precision calculation of critical exponents in the O(N) universality classes with the nonperturbative renormalization group

et al. 2020

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“…Clearly the Meijer-G approximants return accurate estimates of both the mass and field anomalous dimensions as well as their critical exponents η and ν. Note that KP use as resummation a variational perturbation theory approach, and that Guida and Zinn-Justin use a conformal mapping [10,66] 0.5876 0.0310 on top of their Borel-Padé method [10,34]. In contrast, the calculations presented here are straightforward to implement, and delivered these results for the most natural choices of helper functions, which were, in fact, the first and only ones we tried.…”

Section: Anomalous Dimension For Self-avoiding Walks In Three Dimementioning

confidence: 90%

“…Besides adding one extra coefficient to previously computed expansions, their work is an exercise in state-of-the-art practical resummation as well as an excellent compilation of reference results for this important model [34,66]. Furthermore KP give full access to their numerical and analytical expansions in their supplementary material.…”

Section: Anomalous Dimension For Self-avoiding Walks In Three Dimementioning

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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“…However, considerable progress of other techniques has by now produced a multitude of much more refined results. Among those, we like to point out the particularly astonishing performance of the conformal bootstrap program [40,101] and Monte Carlo methods [53,54], which reached unprecedented accuracy in some cases.…”

Section: Introductionmentioning

confidence: 99%

Minimally subtracted six-loop renormalization of O(n) -symmetric ϕ4 theory and critical exponents

Kompaniets¹,

Panzer²

2017

Phys. Rev. D

209

285

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We present the perturbative renormalization group functions of O(n)-symmetric φ 4 theory in 4 − 2ε dimensions to the sixth loop order in the minimal subtraction scheme. In addition, we estimate diagrams without subdivergences up to 11 loops and compare these results with the asymptotic behaviour of the beta function. Furthermore we perform a resummation to obtain estimates for critical exponents in three and two dimensions.

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Scale-free Monte Carlo method for calculating the critical exponentγof self-avoiding walks

Cited by 53 publications

References 30 publications

Precision calculation of critical exponents in the O(N) universality classes with the nonperturbative renormalization group

Precision calculation of critical exponents in the O(N) universality classes with the nonperturbative renormalization group

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

Minimally subtracted six-loop renormalization of O(n) -symmetric ϕ4 theory and critical exponents

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