On integrable directed polymer models on the square lattice

TL;DR

This paper identifies a new two-parameter integrable directed polymer model on the square lattice, expanding the class of exactly solvable models by leveraging recent results on stochastic particle systems and Bethe ansatz techniques.

Contribution

It introduces the Inverse-Beta polymer, a novel integrable directed polymer model, and derives its Bethe ansatz solution, broadening the understanding of integrable stochastic models.

Findings

Discovery of the Inverse-Beta polymer as a new integrable model

Derivation of Bethe ansatz solution for the Inverse-Beta polymer

Extension of integrability conditions to directed polymer models

Abstract

In a recent work Povolotsky provided a three-parameter family of stochastic particle systems with zero-range interactions in one dimension which are integrable by coordinate Bethe ansatz. Using these results we obtain the corresponding condition for integrability of a class of directed polymer models with random weights on the square lattice. Analyzing the solutions we find, besides known cases, a new two-parameter family of integrable DP model, which we call the Inverse-Beta polymer, and provide its Bethe ansatz solution.