Limit Shapes of the Stochastic Six Vertex Model

It is shown that limit shapes for the stochastic 6-vertex model on a cylinder with the uniform boundary state on one end are solutions to the Burger type equation. Solutions to these equations are studied for step initial conditions. When the circumference goes to infinity the solution corresponding...

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Bibliographic Details
Published in:Communications in mathematical physics 2018-11, Vol.363 (3), p.741-765
Main Authors: Reshetikhin, Nicolai, Sridhar, Ananth
Format: Article
Language:English
Subjects:
Classical and Quantum Gravitation
Complex Systems
Cylinders
Initial conditions
Mathematical and Computational Physics
Mathematical models
Mathematical Physics
Physics
Physics and Astronomy
Quantum Physics
Relativity Theory
Theoretical
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Summary:It is shown that limit shapes for the stochastic 6-vertex model on a cylinder with the uniform boundary state on one end are solutions to the Burger type equation. Solutions to these equations are studied for step initial conditions. When the circumference goes to infinity the solution corresponding to critical initial densities coincides with the one found by Borodin, Corwin, and Gorin.
ISSN:0010-3616
1432-0916
DOI:10.1007/s00220-018-3253-2