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]

It is widely expected that, for a large class of models, scale invariance implies conformal invariance. A sufficient condition for this to happen is that there exists no integrated vector operator, invariant under all internal symmetries of the model, with scaling dimension −1. In this article, we compute the scaling dimensions of vector operators with lowest dimensions in the O(N ) model. We use three different approximation schemes: ǫ expansion, large N limit and third order of the Derivative Expansion of Non-Perturbative Renormalization Group equations. We find that the scaling dimensions of all considered integrated vector operators are always much larger than −1. This strongly supports the existence of conformal invariance in this model. For the Ising model, an argument based on correlation functions inequalities was derived, which yields a lower bound for the scaling dimension of the vector perturbations. We generalize this proof to the case of the O(N ) model with N ∈ {2, 3, 4}.

No abstract

No abstract

The search of controlled approximations to study strongly coupled systems remains a very general open problem. Wilson's renormalization group has shown to be an ideal framework to implement approximations going beyond perturbation theory. In particular, the most employed approximation scheme in this context, the derivative expansion, was recently shown to converge and yield accurate and very precise results. However, this convergence strongly depends on the shape of the employed regulator. In this letter we clarify the reason for this dependence and justify, simultaneously, the most largely employed procedure to fix this dependence, the principle of minimal sensitivity.