Remarks on disorder and aperiodicity in a model for interacting polymers

We present a comparative study of the effects of random and aperiodically distributed interactions on the critical behavior of a model for two interacting polymers on a diamond hierarchical lattice. The problem is formulated in terms of exact renormalization-group (RG) recursion relations. In the disordered case, it is possible to develop a perturbative treatment in order to obtain the fixed points of the moments associated with the random distribution of interactions. Fully uncorrelated disorder may become relevant, driving the system away from a homogeneous fixed point. Layered disorder may lead to a breakdown of the perturbative treatment. In the case of aperiodic interactions, we also show some examples of relevance and irrelevance of geometric fluctuations, and further investigate the models by resorting to an independent transfer-matrix (TM) analysis, which fully corroborates the scaling results.