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Precision calculation of critical exponents in the O(N) universality classes with the nonperturbative renormalization group
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Precision calculation of critical exponents in the O(N) universality classes with the nonperturbative renormalization group
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We compute the critical exponents $\nu$, $\eta$ and $\omega$ of $O(N)$ models for various values of $N$ by implementing the derivative expansion of the nonperturbative renormalization group up to next-to-next-to-leading order [usually denoted $\mathcal{O}(\partial^4)$]. 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 $\alpha$, our results are compatible with those of Monte-Carlo but clearly exclude experimental values.
Forward citations
Cited by 4 Pith papers
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Asymptotic behaviour of the derivative expansion in the ERG
The derivative expansion of the exact renormalization group is divergent for generic operators in any dimension, but behaves as an asymptotic series that converges to high order in common applications.
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Rethinking Dimensional Regularization in Critical Phenomena
A new Functional Dimensional Regularization scheme computes Ising critical exponents directly in d=3 with apparently better convergence than standard functional RG approximations.
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Solving Functional Renormalization Group Equations with Neural Networks
A neural network that learns fRG flows from the equation residual, with a large-N analytic baseline, matches finite-difference and discontinuous-Galerkin solvers for O(N) models.
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Functional Dimensional Regularization for O(N) Models
Functional dimensional regularization applied to the O(N) universality class yields critical exponents comparable to advanced non-perturbative methods while retaining efficiency and rapid convergence.
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