Recent advances in the six-vertex model
Filippo Colomo
Abstract
The six-vertex model with domain wall boundary conditions (DWBC) (as opposed to, e.g., periodic boundary conditions (PBC)) is currently undergoing a period of great interest, both for its relationship with the theory of Alternating Sign Matrices and with some tiling problems, and for the fact that bulk quantities are sensitive to boundary conditions even in the thermodynamic limit, due to the effective non locality of interactions in the model. This last question is in turn related to the problem of a sensible definition of thermodynamic limit for such models, and to the so called Arctic Circle Theorem. Although the model is integrable, very few explicit results are known. A detailed asymptotic analysis of the partition function in the thermodynamic limit, while still lacking, would be highly desiderable to address previous issues. We present here a general technique to compute asymptotics of correlators for integrable systems, and some preliminary results from its application to the present problem.
Elenco dei partecipanti al convegno di Bari.