Stochastic symplectic ice

In this paper, we construct solvable ice models (six-vertex models) with stochastic weights and U-turn right boundary, which we term “stochastic symplectic ice”. The models consist of alternating rows of two types of vertices. The probabilistic interpretation of the models leads to novel interacting...

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Bibliographic Details
Published inLetters in mathematical physics Vol. 112; no. 3
Main Author Zhong, Chenyang
Format Journal Article
LanguageEnglish
Published Dordrecht Springer Netherlands 01.06.2022
Springer Nature B.V
Subjects
Apexes
Complex Systems
Functional equations
Geometry
Group Theory and Generalizations
Mathematical and Computational Physics
Mathematical models
Operators (mathematics)
Partitions (mathematics)
Physics
Physics and Astronomy
Theoretical
Colored vertex models
Stochastic symplectic ice
Yang–Baxter equation
Demazure–Lusztig operators of type C
Interacting particle systems
Solvable lattice models
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Summary:In this paper, we construct solvable ice models (six-vertex models) with stochastic weights and U-turn right boundary, which we term “stochastic symplectic ice”. The models consist of alternating rows of two types of vertices. The probabilistic interpretation of the models leads to novel interacting particle systems where particles alternately jump to the right and then to the left. Two colored versions of the models and related stochastic dynamics are also introduced. Using the Yang–Baxter equations, we establish functional equations and recursive relations for the partition functions of these models. In particular, the recursive relations satisfied by the partition function of one of the colored models are closely related to Demazure–Lusztig operators of type C.
ISSN:0377-9017
1573-0530
DOI:10.1007/s11005-022-01547-w