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 $\nu =0.632\mathrm{}$ and to an anomalous dimension $\eta =0.033\mathrm{}$ which is significantly improved compared with lower orders calculations.