Solution of Dyson equation for elastic membranes

The Dyson equation for the renormalization of the curvature stiffness by elastic fluctuations into a simple differential equation is transformed and solved iteratively as well as numerically. If the tension parameter falls below some critical value, the inverse two‐point function develops discontinuously a minimum at a nonzero momentum p₀. This should be relevant for understanding a transition in elastic membranes.