Multicritical unbinding phenomena and nonlinear functional renormalization group

Using a nonlinear functional renormalization-group approach, we study the problem of unbinding phenomena both for interfaces and membranes. Our numerical and analytical solutions of the differential recursion relation confirm the existence of the ‘‘unusual bifurcation’’ of the fixed-point potentials describing unbinding at the upper critical dimension d=${\mathit{d}}^{\mathrm{*}}$. However, in addition to one critical and one purely repulsive potential, we find an infinite family of multicritical potentials bifurcating from the drifting fixed point. The values for the scaling indices, which are singular near ${\mathit{d}}^{\mathrm{*}}$, are calculated here exactly to leading orders in ε=${\mathit{d}}^{\mathrm{*}}$-d and are shown to behave as ${\mathrm{\epsilon }}^{2/3}$.