Exact Solution of the Six-Vertex Model with Domain Wall Boundary Conditions. Critical Line between Ferroelectric and Disordered Phases

2008/02/29 by Pavel Bleher, Karl Liechty
Mathematics · Physics and Astronomy · #Analytic continuation #Boundary (topology) #Boundary value problem #Combinatorics #Condensed matter physics #Critical line #Domain (mathematical analysis) #Ferroelectricity #Geometry #Line (geometry) #Mathematical analysis #Mathematical physics #Mathematics #Partition (number theory) #Partition function (quantum field theory) #Physics #Quantum mechanics #Random Matrices and Applications #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #Vertex (graph theory) #Vertex model #math-ph #math.MP #msc:82B20

paper · pdf · doi:10.1007/s10955-009-9688-2

22 pages, 6 figures, to appear in the Journal of Statistical Physics

arxiv created 2008/06/26 · openalex publication_date 2009/02/01 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

Abstract

This is a continuation of the papers [4] of Bleher and Fokin and [5] of Bleher and Liechty, in which the large n asymptotics is obtained for the partition function Z_n of the six-vertex model with domain wall boundary conditions in the disordered and ferroelectric phases, respectively. In the present paper we obtain the large n asymptotics of Z_n on the critical line between these two phases.

Citations

• Local statistics for random domino tilings of the Aztec diamond
• The Influence of Boundary Conditions in the Six-Vertex Model
• Dimers and amoebae
• Calculation of norms of Bethe wave functions
• Large n Limit of Gaussian Random Matrices with External Source, Part III: Double Scaling Limit