Non-linear interaction in random matrix models of RNA

A non-linear Penner type interaction is introduced and studied in the random matrix model of homo-RNA. The asymptotics in length of the partition function is discussed for small and large $N$ (size of matrix). The interaction doubles the coupling ($v$) between the bases and the dependence of the combinatoric factor on ($v,N$) is found. For small $N$, the effect of interaction changes the power law exponents for the secondary and tertiary structures. The specific heat shows different analytical behavior in the two regions of $N$, with a peculiar double peak in its second derivative for N=1 at low temperature. Tapping the model indicates the presence of multiple solutions.