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arXiv · 2309.04897

Stationary measures for higher spin vertex models on a strip

Zongrui Yang
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Abstract

We introduce a higher spin vertex model on a strip with fused vertex weights. This model can be regarded as a generalization of both the unfused six-vertex model on a strip arXiv:2212.09111 and an 'integrable two-step Floquet dynamics' model introduced in arXiv:1711.08884. We solve for the stationary measure using a fused version of the matrix product ansatz and then characterize it in terms of the Askey-Wilson process. Using this characterization, we obtain the limits of the mean density along an arbitrary down-right path. It turns out that all these models share a common phase diagram, which, after an appropriate mapping, matches the phase diagram of open ASEP. This provides evidence for the universality of this phase diagram.

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Zongrui Yang. 2023-09-09. Stationary measures for higher spin vertex models on a strip. https://arxiv.org/abs/2309.04897

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