Directed polymers and randomness

  title={Directed polymers and randomness},
  author={Somendra M Bhattacharjee},
1 Citations
Random Walks and Polymers in the Presence of Quenched Disorder
After a general introduction to the field, we describe some recent results concerning disorder effects on both ‘random walk models’, where the random walk is a dynamical process generated by local


Diffusion of directed polymers in a random environment
We consider a system of random walks or directed polymers interacting weakly with an environment which is random in space and time. In spatial dimensionsd>2, we establish that the behavior is
On the glassy nature of random directed polymers in two dimensions
We study numerically directed polymers in a random potential in 1 + 1 dimensions. We introduce two copies of the polymer, coupled through a thermodynamic local interaction. We show that the system is
Thermal properties of directed polymers in a random medium.
  • Derrida, Golinelli
  • Materials Science
    Physical review. A, Atomic, molecular, and optical physics
  • 1990
We calculate, by performing a product of random matrices, the specific heat and its derivative for the problem of directed polymers in a random medium. Our results are consistent with the existence
Phase transitions and noise cross-correlations in a model of directed polymers in a disordered medium
  • Basu
  • Materials Science
    Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics
  • 2000
We show that effective interactions mediated by disorder between two directed polymers can be modeled as the cross-correlation of noises in the Kardar-Parisi-Zhang (KPZ) equations satisfied by the
The Theory of Polymer Dynamics
Introduction Static properties of polymers Brownian motion Dynamics of flexible polymers in dilute solution Many chain systems Dynamics of a polymer in a fixed network Molecular theory for the
Infinite number of exponents for a spin-glass transition.
It is shown that an infinite number of exponents is required to describe these overlaps of m(g~2) paths at the spin-glass transition for a directed polymer in a random medium in an $\ensuremath{\epsilon}=d\ensure Math{-}2$ expansion without using the replica trick.
Polymers on disordered trees, spin glasses, and traveling waves
We show that the problem of a directed polymer on a tree with disorder can be reduced to the study of nonlinear equations of reaction-diffusion type. These equations admit traveling wave solutions
Polymers on disordered hierarchical lattices: A nonlinear combination of random variables
The problem of directed polymers on disordered hierarchical and hypercubic lattices is considered. For the hierarchical lattices the problem can be reduced to the study of the stable laws for
Directed paths in a random potential.
  • Fisher, Huse
  • Physics
    Physical review. B, Condensed matter
  • 1991
The properties of directed paths in random media are explored, with emphasis on the low-temperature phase, and it is argued that at fixed temperature, the possible states of a directed path in an infinite system with one end fixed are simply parametrized by its average orientation.