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

被引：0
作者：
Pavel Bleher
Karl Liechty
机构：
[1] Indiana University-Purdue University Indianapolis,Department of Mathematical Sciences
来源：
Journal of Statistical Physics | 2009年 / 134卷
关键词：
Six-vertex model; Domain wall boundary conditions; Critical line between ferroelectric and disordered phases; Large ; asymptotics of the partition function;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
This is a continuation of the papers of Bleher and Fokin (Commun. Math. Phys., 268:223–284, 2006) and of Bleher and Liechty (Commun. Math. Phys., 286:777–801, 2009), in which the large n asymptotics is obtained for the partition function Zn 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 Zn on the critical line between these two phases.
引用
收藏
相关论文
共 44 条
  • [1] Allison D.(2005)Numerical study of the 6-vertex model with domain wall boundary conditions Ann. Inst. Fourier (Grenoble) 55 1847-1869
  • [2] Reshetikhin N.(1995)Exact solution and interfacial tension of the six-vertex model with anti-periodic boundary conditions J. Phys. A 28 2759-2770
  • [3] Batchelor M.T.(2006)Exact solution of the six-vertex model with domain wall boundary conditions. Disordered phase Commun. Math. Phys. 268 223-284
  • [4] Baxter R.J.(2007)Large n limit of Gaussian random matrices with external source, part III: Double scaling limit Commun. Math. Phys. 270 481-517
  • [5] O’Rourke M.J.(2009)Exact solution of the six-vertex model with domain wall boundary conditions Commun. Math. Phys. 286 777-801
  • [6] Yung C.M.(1996)Local statistics for random domino tilings of the Aztec diamond Duke Math. J. 85 117-166
  • [7] Bleher P.M.(2005)Square ice, alternating sign matrices, and classical orthogonal polynomials J. Stat. Mech. Theory Exp. 1 005-1109
  • [8] Fokin V.V.(1999)Diamond ice J. Stat. Phys. 96 1091-10306
  • [9] Bleher P.M.(2006)Domino tilings and the six-vertex model at its free fermion point J. Phys. A, Math. Gen. 39 10297-333
  • [10] Kuijlaars A.B.J.(1987)Partition function of the six-vertex model in a finite volume Dokl. Akad. Nauk SSSR 297 331-4334
12345