Thermodynamic limit of the six-vertex model with domain wall boundary conditions
By V. Korepin, P. Zinn-Justin. 2000
158 citations recorded by the source corpus.
We address the question of the dependence of the bulk free energy on boundary conditions for the six-vertex model. Here we compare the bulk free energy for periodic and domain wall boundary conditions. Using a determinant representation for the partition function with domain wall boundary conditions, we derive Toda differential equations and solve them asymptotically in order to extract the bulk free energy. We find that it is different and bears no simple relation to the free energy for periodic boundary conditions. The six-vertex model with domain wall boundary conditions is closely related to algebraic combinatorics (alternating sign matrices). This implies new results for the weighted counting for large-size alternating sign matrices. Finally, we comment on the interpretation of our results, in particular in connection with domino tilings (dimers on a square lattice).
Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology, Statistics and Probability
View Paper: https://www.semanticscholar.org/paper/9af25404582537d4d4eed6ed89131d11e9da1980
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In Discrete Mathematics and Combinatorics
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Citations in the corpus
- Non-intersecting paths, random tilings and random matrices (2000, background): “[7], [16], [19], [21], [20], [30], [44], [49], [69] and [70] Connections between random permutations and the so called random turns model, which gives certain non-intersecting paths has beeen discussed in [1], [22], and [23].”