On the Bethe ansatz for random directed polymers

Somendra M. Bhattacharjee, Sutapa Mukherji

Lennaert VAN VEEN

Victor S Dotsenko

The two-time free energy distribution function in one-dimensional directed polymers in a random potential is derived in terms of the Bethe ansatz replica technique by mapping the replicated problem to the N -particle quantum boson system with attractive interactions.

Tsuyoshi Horiguchi

Sen Mu, Abbas Ali Saberi, Mehran Kardar A

A finite density of mutually avoiding directed polymers in a quenched random medium is a minimal model of glassy line matter. The dilute theory, solved by replica Bethe ansatz, predicts an interaction free energy proportional to $ρ^2$ and disorder cumulants with distinct power-law dependences on the density $ρ$, but direct numerical tests have been hindered by the combinatorially large many-polymer transfer matrix. We recast the problem as filling logarithmic eigenvalues of a single-polymer transfer-matrix product, obtaining the quenched free energy, its cumulants, and a disorder-induced linear spectral edge consistent with the replica prediction.

Yi‐Cheng Zhang