Stationary measures for higher spin vertex models on a strip

2023/09/09 by Yang, Zongrui
#FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Probability (math.PR)

paper · doi:10.48550/arxiv.2309.04897

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 [Yan22] and an 'integrable two-step Floquet dynamics' model introduced in [Van18]. 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, thereby establishing a universality result for this phase diagram.

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