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Exact Solutions to the Six-Vertex Model with Domain Wall Boundary Conditions and Uniform Asymptotics of Discrete Orthogonal Polynomials on an Infinite Lattice
Statistical Mechanics Random Matrices Orthogonal Polynomials Asymptotics Riemann-Hilbert Problems
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2015/1/19
In this dissertation the partition function, $Z_n$, for the six-vertex model with domain wall boundary conditions is solved in the thermodynamic limit in various regions of the phase diagram. In the f...
Algebraic arctic curves in the domain-wall six-vertex model
Algebraic arctic domain-wall six-vertex model
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2011/1/20
The arctic curve, i.e. the spatial curve separating ordered (or ‘frozen’) and disordered (or ‘temperate) regions, of the six-vertex model with domain wall boundary conditions is discussed for the root...
A new representation for the partition function of the six vertex model with domain wall boundaries
Mathematical Physics (math-ph) Statistical Mechanics (cond-mat.stat-mech) Exactly Solvable and Integrable Systems (nlin.SI)
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2010/11/11
We obtain a new representation for the partition function of the six vertex model with domain wall boundaries using a functional equation recently derived by the author. This new representation is giv...
Solutions of the Yang-Baxter equation: descendants of the six-vertex model from the Drinfeld doubles of dihedral group algebras
Yang-Baxter equation six-vertex model dihedral group algebras
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2010/4/6
The representation theory of the Drinfeld doubles of dihedral groups is used to solve the Yang-Baxter equation. Use of the 2-dimensional representations recovers the six-vertex model solution. Solutio...
Functional relations for the six vertex model with domain wall boundary conditions
Functional relations six vertex model domain wall boundary
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2010/4/2
In this work we demonstrate that the Yang-Baxter algebra can also be employed in order to derive a functional relation for the partition function of the six vertex model with domain wall boundary cond...
Coordinate space wave function from the Algebraic Bethe Ansatz for the inhomogeneous six-vertex model
space wave function Algebraic Bethe Ansatz inhomogeneous six-vertex model
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2010/4/1
We derive the coordinate space wave function for the inhomogeneous six-vertex model from the Algebraic Bethe Ansatz. The result is in agreement with the result first obtained long time ago by Yang and...