Mapping the non-directed polymer model to a non-linear growth equation of Burgers type

We study the non-directed polymer model (NDP model) in the framework of a non-linear growth equation of Burgers type [Kardar–Parisi–Zhang equation with quenched noise (KPZQN equation)] by means of path integrals. The scaling exponents for the KPZQN equation are expressed in terms of the NDP model. In the strong-coupling regime, at low-temperatures, the “tadpole” conformation seems to be reasonable for the polymer. The “tadpole” is discussed in the context of interfaces in a strong-coupling regime where the noise dominates. We find that the “tadpole” behavior corresponds to structural “avalanches” of the interface, whereupon a totally new topology occurs. This restructuring is followed by periods of conservation of shape where the interface is “waiting” for new energetically more profitable structures.