Nonperturbative renormalization group approach to the Ising model: a derivative expansion at order $\partial^4$

On the example of the three-dimensional Ising model, we show that nonperturbative renormalization group equations allow one to obtain very accurate critical exponents. Implementing the order $\partial^4$ of the derivative expansion leads to $\nu=0.632$ and to an anomalous dimension $\eta=0.033$ which is significantly improved compared with lower orders calculations.