scholarly journals The Many Faces of the Chiral Potts Model

1997 ◽  
Vol 11 (01n02) ◽  
pp. 11-26 ◽  
Author(s):  
Helen Au-Yang ◽  
Jacques H.H. Perk
Keyword(s):  
Quantum Groups ◽  
Potts Model ◽  
Hypergeometric Functions ◽  
Chiral Potts Model ◽  
Root Of Unity ◽  
Basic Hypergeometric Functions ◽  
Higher Genus ◽  
The Many

In this talk, we give a brief overview of several aspects of the theory of the chiral Potts model, including higher-genus solutions of the star–triangle and tetrahedron equations, cyclic representations of affine quantum groups, basic hypergeometric functions at root of unity, and possible applications.

GAUSSIAN ORTHOGONAL ENSEMBLE FOR THE LEVEL SPACING STATISTICS OF THE QUANTUM FOUR-STATE CHIRAL POTTS MODEL

2002 ◽  
Vol 16 (14n15) ◽  
pp. 2047-2053
Author(s):  
J.-Ch. ANGLÈS d'AURIAC ◽  
S. DOMMANGE ◽  
J.-M. MAILLLARD ◽  
C. M. VIALLET
Keyword(s):  
Random Matrix ◽  
Potts Model ◽  
Matrix Theory ◽  
Level Spacing ◽  
Chiral Potts Model ◽  
Quantum Chain ◽  
Ensemble Statistics ◽  
Higher Genus ◽  
Gaussian Orthogonal Ensemble ◽  
Potts Chain

We have performed a Random Matrix Theory (RMT) analysis of the quantum four state chiral Potts chain for different sizes of the quantum chain up to eight sites, and for different unfolding methods. Our analysis shows that one generically has a Gaussian Orthogonal Ensemble statistics for the unfolded spectrum instead of the GUE statistics one could expect. Furthermore a change from the generic GOE distribution to a Poisson distribution occurs when the hamiltonian becomes integrable. Therefore, the RMT analysis can be seen as a detector of "higher genus integrability".

scholarly journals Random matrix theory and higher genus integrability: the quantum chiral Potts model

2002 ◽  
Vol 35 (23) ◽  
pp. 4801-4822 ◽  
Author(s):  
J-Ch Angl$egrave$s d$apos$Auriac ◽  
J-M Maillard ◽  
C M Viallet
Keyword(s):  
Random Matrix Theory ◽  
Random Matrix ◽  
Potts Model ◽  
Matrix Theory ◽  
Chiral Potts Model ◽  
Higher Genus
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