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On integrable directed polymer models on the square lattice

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arxiv 1506.05006 v2 pith:W34HVABL submitted 2015-06-16 cond-mat.dis-nn cond-mat.stat-mech

Thimothée Thiery , Pierre Le Doussal This is my paper · ORCID
classification cond-mat.dis-nncond-mat.stat-mech
keywords integrablepolymeransatzbethedirectedfamilylatticemodels
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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.

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    Inhomogeneous spin q-Whittaker polynomials are orthogonal under an explicit torus scalar product, giving a basis of symmetric polynomials.

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