Polymer models with competing collapse interactions

We study a lattice polymer model that incorporates as special cases two different models previously studied in the literature, namely, the Wu-Bradley model and the asymmetric interacting self-avoiding trail (AISAT) model. Both models are characterized by the presence of different microscopic interactions, driving different collapse transitions. Our motivation is that, while the phase diagram and universality classes occurring in the former model are rather well established, some contradictory results have recently emerged for the latter. We consider a square Husimi lattice, which is expected to best approximate the model on the ordinary 2d square lattice. Even though such (mean-field-like) calculations do not provide information about critical exponents for the corresponding finite-dimensional model, the phase diagram can be worked out with high numerical precision. Our results show that the phase diagrams of the two aforementioned models are fully equivalent from the topological point of view. Heuristic arguments, and the availability of exact results in certain limit cases, lead us to conjecture that such an equivalence might extend to the finite-dimensional case and the related universality classes.