A Spectral Route to Directed-Polymer Glasses

Sen Mu; Abbas Ali Saberi; Mehran Kardar

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arXiv · 2608.03730

A Spectral Route to Directed-Polymer Glasses

Sen Mu·Abbas Ali Saberi·Mehran Kardar

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Abstract

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.

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Sen Mu, Abbas Ali Saberi, Mehran Kardar. 2026-08-04. A Spectral Route to Directed-Polymer Glasses. https://arxiv.org/abs/2608.03730

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