Phase transitions and noise cross-correlations in a model of directed polymers in a disordered medium
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 respective free energies of these polymers. When there are two polymers, disorder introduces attractive interactions between them. We analyze the phase diagram in detail and show that these interactions lead to new phases in the phase diagram. We show that, even in dimension d=1, the two directed polymers see the attraction only if the strength of the disorder potential exceeds a threshold value. We extend our calculations to show that if there are m polymers in the system, then m-body interactions are generated in the disorder averaged effective free energy.
Basu
A
Centre for Condensed Matter Theory, Department of Physics, Indian Institute of Science, Bangalore 560012, India and Poornaprajna Institute of Scientific Research, Bangalore, India.