We report on progress towards an attempt to understand the representations of infinite dimensional groups that arise from quantum field theories on Riemann surfaces. We consider some examples that arise from the correspondence between chiral Potts integrable models and monopoles established by Atiyah and Murray and explore the Fermi-Bose correspondence on a general Riemann surface. Mathematics ...

We discuss some algebraic setting of chiral SU (N) K models in terms of the satistical dimensions of their fields. In particular, the conformal dimensions and the central charge of the chiral SU (N) K models are calculated from their braid matrices. Furthermore, at level K = 2, we present the characteristic polynomials of their fusion matrices in a factored form.

We establish the Bethe equation of the τ -model in the N -state chiral Potts model (including the degenerate selfdual cases) with alternating vertical rapidities. The eigenvalues of a finite-size transfer matrix of the chiral Potts model are computed by use of functional relations. The significance of the ”alternating superintegrable” case of the chiral Potts model is discussed, and the degener...

We demonstrate that the τ (j)-matrices in the superintegrable chiral Potts model possess the Onsager algebra symmetry for their degenerate eigenvalues. The Fabricius-McCoy comparison of functional relations of eight-vertex model for roots of unity and superintegrable chiral Potts model has been carefully analyzed by identifying equivalent terms in the corresponding equations , by which we extra...

Recent advances in graphene-nanoribbon-based research have demonstrated the controlled synthesis of chiral graphene nanoribbons (chGNRs) with atomic precision using strategies of on-surface chemistry. However, their electronic characterization, including typical figures of merit like band gap or frontier band's effective mass, has not yet been reported. We provide a detailed characterization of...

The chiral Potts model continues to pose particular challenges in statistical mechanics: it is “exactly solvable” in the sense that it satisfies the Yang-Baxter relation, but actually obtaining the solution is not easy. Its free energy was calculated in 1988 and the order parameter was conjectured in full generality a year later. However, a derivation of that conjecture had to wait until 2005. ...

We find the rules which count the energy levels of the 3 state superintegrable chiral Potts model and demonstrate that these rules are complete. We then derive the complete spectrum of excitations in the thermodynamic limit in the massive phase and demonstrate the existence of excitations which do not have a quasi-particle form. The physics of these excitations is compared with the BCS supercon...

In this paper we study the large-N limits of the integrable N-state chiral Potts model. Three chiral solutions of the star-triangle equations are derived, with states taken from all integers, or from a finite or infinite real interval. These solutions are expected to be chiral-field lattice deformations of parafermionic conformal field theories. A new two-sided hypergeometric identity is derive...