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Domain Wall Six-Vertex Model with Half-Turn Symmetry

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Abstract

We obtain asymptotic formulas for the partition function of the six-vertex model with domain wall boundary conditions and half-turn symmetry in each of the phase regions. The proof is based on the Izergin–Korepin–Kuperberg determinantal formula for the partition function and its reduction to orthogonal polynomials, and on an asymptotic analysis of the orthogonal polynomials under consideration in the framework of the Riemann–Hilbert approach.

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Notes

  1. There is a typo in [7, Equation (6.3.54)]. All integrals after the first line should be from 0 to \(\infty \), not \(-\infty \) to \(\infty \). The value of the integral, however, is given correctly.

  2. There is a typo in [7, Equation (6.6.16)]. \(z_j\) should be replaced with \(y_j\), and the definition of \(y_j\) should be made earlier.

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Authors and Affiliations

  1. Department of Mathematical Sciences, Indiana University-Purdue University Indianapolis, 402 N. Blackford St., Indianapolis, IN, 46202, USA

    Pavel Bleher

  2. Department of Mathematical Sciences, DePaul University, Chicago, IL, 60614, USA

    Karl Liechty

Authors
  1. Pavel Bleher
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  2. Karl Liechty
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Correspondence to Karl Liechty.

Additional information

Communicated by Peter J. Forrester.

This work was performed during the program Statistical Mechanics and Combinatorics at the Simons Center for Geometry and Physics in March 2016. The authors are grateful for the hospitality of the Simons Center. KL would like to thank T. Kyle Petersen for helpful discussions. PB is supported in part by the National Science Foundation (NSF) Grants DMS-1265172 and DMS-1565602. KL is supported by a grant from the Simons Foundation (#357872).

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Bleher, P., Liechty, K. Domain Wall Six-Vertex Model with Half-Turn Symmetry. Constr Approx 47, 141–162 (2018). https://doi.org/10.1007/s00365-017-9405-3

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  • DOI: https://doi.org/10.1007/s00365-017-9405-3

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