Influence of spatial correlation for directed polymers

Directed polymers versus directed percolation

Universality plays a central role within the rubric of modern statistical mechanics, wherein an insightful continuum formulation rises above irrelevant microscopic details, capturing essential scaling behaviors. Nevertheless, occasions do arise where the lattice or another discrete aspect can constitute a formidable legacy. Directed polymers in random media, along with its close sibling, direct...

Theory of directed polymers.

We develop a theory of polymers in a nematic solvent by exploiting an analogy with two-dimensional quantum bosons at zero temperature. We argue that the theory should also describe polymers in an isotropic solvent. The dense phase is analyzed in a Bogoliubovlike approximation, which assumes a broken symmetry in the phase of the boson order parameter. We find a stiffening of the longitudinal flu...

Directed polymers and Randomness

The effects of two types of randomness on the behaviour of directed polymers are discussed in this chapter. The first part deals with the effect of randomness in medium so that a directed polymer feels a random external potential. The second part deals with the RANI model of two directed polymers with heterogeneity along the chain such that the interaction is random. The random medium problem i...

Flory approximation for directed branched polymers and directed percolation

Dimensional Reduction for Directed Branched Polymers

Dimensional reduction occurs when the critical behavior of one system can be related to that of another system in a lower dimension. We show that this occurs for directed branched polymers (DBP) by giving an exact relationship between DBP models in D+1 dimensions and repulsive gases at negative activity in D dimensions. This implies relations between exponents of the two models: γ(D + 1) = α(D)...