Peculiarity of the Coulombic criticality ?

International audienceWe study the Coulombic criticality of ionic fluids within the restricted primitive model (RPM). We indicate that for the RPM, analysed in terms of the field of charge density, the corresponding Landau-Ginzburg-Wilson effective Hamiltonian has a negative $\varphi ^{4}$-coefficient. In that case, solving the ``exact'' renormalization group equation in the local potential approximation, we show that close initial Hamiltonians may lead either to a first order transition or to an Ising-like critical behavior, the partition being formed by the tri-critical surface. This situation apparently illustrates the theoretical wavering encountered in the literature concerning the nature of the Coulombic criticality. Nevertheless, it is most probable that, in terms of the field considered, the model does not display any criticality