For distribution - thanks

[CM ICTP - Trieste]

JOINT ICTP/SISSA STATISTICAL PHYSICS SEMINAR




Tuesday, 5 February    -    12:30 hrs.




Lecture Room 'D' - SISSA Main Building




F. COLOMO   ( INFN, Florence )



" Arctic curves for the Domain Wall Six-Vertex Model "



Abstract

The Arctic Circle Theorem (Jockusch-Propp-Shor) concerns a model of 
domino tiling with peculiar boundary conditions, exhibiting phase 
separation, with the emergence of `limit shapes' and `arctic curves'. 
The computation of such objects, and the characterization of their 
fluctuations, has been performed for several other models (Propp, 
Kenyon, Reshetikhin, Okounkov), with deep implication in algebraic 
combinatorics and algebraic geometry. However all such models can be 
viewed as models of dimers, i.e. of discrete free fermions. The most 
natural generalization of such models, including an interaction, is 
provided by the Domain Wall Six-Vertex Model. We here derive, for this 
model with generic values of its parameter, the exact analytic 
expression of the arctic curves, and characterize their fluctuations, 
thus extending the Arctic Circle Theorem beyond the dimer (free 
fermion) case.