Integrability of Limit Shapes of the Inhomogeneous Six Vertex Model
In this paper we prove that the Euler-Lagrange equations for the limit shape for the inhomogeneous six vertex model on a cylinder have infinitely many conserved quantities.
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arXiv subjects
Ananth Sridhar
Publications and source records attributed to Ananth Sridhar.
Random Tilings with the GPU
We present GPU accelerated implementations of Markov chain algorithms to sample random tilings, dimers, and the six-vertex model.
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Commutativity in Lagrangian and Hamiltonian Mechanics
The main result of this note is a characterization of the Poisson commutativity of Hamilton functions in terms of their principal action functions.
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Abelian Higgs Vortices and Discrete Conformal Maps
We establish a connection between recent developments in the study of vortices in the abelian Higgs models, and in the theory of structure-preserving discrete conformal maps. We explain how both are related via conformal mapping problems involving prescribed linear combinations of the curvature and volume form, and show how the discrete conformal theory can be used to construct discrete vortex solutions.
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Limit Shapes of the Stochastic Six Vertex Model
We show 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 of the cylinder goes to infinity the solution corresponding to critical initial densities coincides with the one found by Borodin, Corwin and Gorin.
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Integrability of Limit Shapes of the Six Vertex Model
The main result of this paper is the construction of infinitely many conserved quantities (corresponding to commuting transfer-matrices) for the limit shape equation for the 6-vertex model on a cylinder. This suggests that the limit shape equation is an integrable PDE with gradient constraints. At the free fermionic point this equation becomes the complex Burgers equation.
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Asymptotic Determinant of Discrete Laplace-Beltrami Operators
We study combinatorial Laplacians on rectangular subgraphs of $ ε\mathbb{Z}^2 $ that approximate Laplace-Beltrami operators of Riemannian metrics as $ ε\rightarrow 0 $. These laplacians arise as follows: we define the notion of a Riemmanian metric structure on a graph. We then define combinatorial free field theories and describe how these can be regarded as finite dimensional approximations of scalar field theory. We focus on the Gaussian field theory on rectangular subgraphs of $ \mathbb{Z}^2 $ and study its partition function by computing the asymptotic determinant of the discrete laplacian.
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