On integrable directed polymer models on the square lattice

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.

31 pages, 2 figures, 4 appendix

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• Midpoint distribution of directed polymers in the stationary regime: exact result through linear response
• Mutually avoiding paths in random media and largests eigenvalues of random matrices
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• Log-gamma directed polymer with one free end via coordinate Bethe Ansatz
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