4 research outputs found
A classification of four-state spin edge Potts models
We classify four-state spin models with interactions along the edges
according to their behavior under a specific group of symmetry transformations.
This analysis uses the measure of complexity of the action of the symmetries,
in the spirit of the study of discrete dynamical systems on the space of
parameters of the models, and aims at uncovering solvable ones. We find that
the action of these symmetries has low complexity (polynomial growth, zero
entropy). We obtain natural parametrizations of various models, among which an
unexpected elliptic parametrization of the four-state chiral Potts model, which
we use to localize possible integrability conditions associated with high genus
curves.Comment: 5 figure
Random Matrix Theory and higher genus integrability: the quantum chiral Potts model
We perform a Random Matrix Theory (RMT) analysis of the quantum four-state
chiral Potts chain for different sizes of the chain up to size L=8. Our
analysis gives clear evidence of a Gaussian Orthogonal Ensemble statistics,
suggesting the existence of a generalized time-reversal invariance.
Furthermore a change from the (generic) GOE distribution to a Poisson
distribution occurs when the integrability conditions are met. The chiral Potts
model is known to correspond to a (star-triangle) integrability associated with
curves of genus higher than zero or one. Therefore, the RMT analysis can also
be seen as a detector of ``higher genus integrability''.Comment: 23 pages and 10 figure