Systematic Field Theory of the RNA Glass Transition

We prove that the Lässig-Wiese (LW) field theory for the freezing transition of the secondary structure of random RNA is renormalizable to all orders in perturbation theory. The proof relies on a formulation of the model in terms of random walks and on the use of the multilocal operator product expansion. Renormalizability allows us to work in the simpler scheme of open polymers, and to obtain the critical exponents at 2-loop order. It also allows us to prove some exact exponent identities, conjectured by LW.

Figure 1

Results for ${\theta }^{*}$ (black) and ${\rho }^{*}$ (gray) at 1- (dashed) and 2-loop (solid) order.