Calculation of the constant factor in the six-vertex model
Pavel Bleher
Indiana University Purdue University Indianapolis, USAThomas Bothner
Université de Montréal, Canada
Abstract
We calculate explicitly the constant factor in the large asymptotics of the partition function of the six-vertex model with domain wall boundary conditions on the critical line between the disordered and ferroelectric phases. On the critical line the weights of the model are parameterized by a parameter , as , , . The asymptotics of on the critical line was obtained earlier in the paper [8] of Bleher and Liechty: , where and are given by explicit expressions, but the constant factor was not known. To calculate the constant , we find, by using the Riemann–Hilbert approach, an asymptotic behavior of in the double scaling limit, as and tend simultaneously to in such a way that . Then we apply the Toda equation for the tau-function to find a structural form for , as a function of , and we combine the structural form of and the double scaling asymptotic behavior of to calculate .
Cite this article
Pavel Bleher, Thomas Bothner, Calculation of the constant factor in the six-vertex model. Ann. Inst. Henri Poincaré Comb. Phys. Interact. 1 (2014), no. 4, pp. 363–427
DOI 10.4171/AIHPD/11