Title: Directed polymers and interfaces in disordered media and models on random networks

Abstract

The investigation of statistical mechanics of disordered systems, random surfaces and membranes has developed a wide set of rigorous and heuristic techniques that have shown a vast space of applicability and rich phenomenology. One of the simplest example of a tethered surfaces are the polymers. In this work we consider field theory formulation for directed polymers and interfaces in presence of quenched disorder. We use the Distributional Zeta Function Method (DZFM) to obtain the average free energy. Under this formalism this quantity is represented as a series of integer moments of the partition function of the model. The structure of field space is analyzed for polymers and interfaces at finite temperature using the saddle-point equations derived from each integer moments of the partition function. For the case of an interface we obtain the wandering exponent also obtained by conventional replica method. Additionally, we study polymers models on random networks, where a pair of polymers on adjacent sites carries a weight factor ω for each link. We relate the network topology and the partition function present in DZFM by using the spectral, disorder and Hamiltonian structure of the system in order to explore the phase diagram, critical behavior, finite-temperature, and finite-size corrections. These kind of models are relevant in polymer science and bioinspired materials.