ARCTIC CURVES OF THE SIX-VERTEX MODEL ON GENERIC DOMAINS: THE TANGENT METHOD

• Published in: Journal of Statistical Physics
• Main Authors: Colomo, F., Sportiello, A.
• Other Authors: Istituto Nazionale di Fisica Nucleare, Sezione di Firenze (INFN, Sezione di Firenze), Istituto Nazionale di Fisica Nucleare (INFN), Université Sorbonne Paris Nord
• Format: Article in Journal/Newspaper
• Language: English
• Published: HAL CCSD 2016
• Subjects: [PHYS.COND.CM-GEN]Physics [physics]/Condensed Matter [cond-mat]/Other [cond-mat.other]; Arctic; Ice Point
• Online Access: https://hal.archives-ouvertes.fr/hal-03210251; https://hal.archives-ouvertes.fr/hal-03210251/document; https://hal.archives-ouvertes.fr/hal-03210251/file/1605.01388_hal.pdf; https://doi.org/10.1007/s10955-016-1590-0

International audience We revisit the problem of determining the Arctic curve in the six-vertex model with domain wall boundary conditions. We describe an alternative method, by which we recover the previously conjectured analytic expression in the square domain. We adapt the method to work for a large class of domains, and for other models exhibiting limit shape phenomena. We study in detail some examples, and derive, in particular, the Arctic curve of the six-vertex model in a triangoloid domain at the ice-point.