Exact solution of a RNA-like polymer model on the Husimi lattice

We investigate a two-tolerant polymer model on the square Husimi lattice, which aims at describing the properties of RNA-like macromolecules. We solve the model in a numerically exact way, working out the grand-canonical phase diagram, both with and without taking into account the stacking effect. Besides a nonpolymerized phase, we observe two different polymerized phases characterized by a lower or higher density of doubly visited lattice bonds. The system exhibits three qualitatively different regimes, as a function of the monomer chemical potential. Below some T-1 temperature and above some T-2 temperature, the transition to the nonpolymerized phase is continuous, whereas, in the (T-1,T-2) temperature range, the transition is first order. In the dilute-solution limit, the high temperature regime corresponds to a swollen ('coil') state, the intermediate regime to a moderately collapsed ('molten') state, with a small fraction of paired segments, and the low temperature regime to an almost fully paired ('native') state. The molten state ends in a tricritical (Theta-like) transition at high temperature and in a critical end point at low temperature. Upon increasing the stacking energy parameter, the temperature range of the molten state turns out to be progressively reduced but never completely removed.