2020/01/21 by Gonzalo De Polsi, Ivan Balog, Matthieu Tissier +1 · 3 citations
Physics and Astronomy · #cond-mat.stat-mech #hep-th
paper · pdf · doi:10.1103/physreve.101.042113
published as Phys. Rev. E 101, 042113 (2020)
arxiv created 2020/01/21 · arxiv updated 2020/04/30
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-next-to-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.