Atsuo Kuniba

FUNCTIONAL RELATIONS IN SOLVABLE LATTICE MODELS I: FUNCTIONAL RELATIONS AND REPRESENTATION THEORY

We study a system of functional relations among a commuting family of row-to-row transfer matrices in solvable lattice models. The role of exact sequences of the finite-dimensional quantum group modules is clarified. We find a curious phenomenon where the solutions of those functional relations also solve the so-called thermodynamic Bethe ansatz equations in the high temperature limit for sl(r+1) models. Based on this observation, we propose possible functional relations for models associated with all the simple Lie algebras. We show that these functional relations certainly fulfill strong constraints coming from the fusion procedure analysis. The application to the calculations of physical quantities will be presented in the subsequent paper.

FUNCTIONAL RELATIONS IN SOLVABLE LATTICE MODELS II: APPLICATIONS

Reported are two applications of the functional relations (T system) among a commuting family of row-to-row transfer matrices proposed in the previous paper (Part I). For a general simple Lie algebra Xr, we determine the correlation lengths of the associated massive vertex models in the antiferroelectric regime and central charges of the RSOS models in two critical regimes. The results reproduce known values or even generalize them, demonstrating the efficiency of the T system.

Spectra in conformal field theories from the Rogers dilogarithm

We propose a system of functional relations having a universal form connected to the Bethe ansatz equation. Based on the analysis of it, we conjecture a new sum formula for the Rogers dilogarithm function in terms of the scaling dimensions of the parafermion conformal field theory.

Thermodynamics of the Uq(Xr(1)) Bethe ansatz system with q a root of unity

The Bethe ansatz equations connected to the Uq(Xr(1))algebra are studied at q = exp(2πi(l + g)), with l being a level and g the dual Coxeter number. Based on a “string hypothesis” in the thermodynamic limit, the central charges relevant to the Xr(1) restricted solid-on-solid models and their fusion hierarchies are determined in two critical regimes. The calculation leads naturally to a generalized conjecture on the Rogers dilogarithmic function identity for an arbitrary pair (Xr(1), l), which includes the earlier one for the simply-laced cases Xr(1) = Ar(1), Dr(1) and E6,7,8(1).

CHARACTERS IN CONFORMAL FIELD THEORIES FROM THERMODYNAMIC BETHE ANSATZ

We propose a new

Exact solution of solid-on-solid models for twisted affine Lie algebras A2n(2) and A2n−1(2)

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Ferro- and antiferro-magnetizations in RSOS models

-series formula for a character of parafermion conformal field theories associated to arbitrary non-twisted affine Lie algebra

Temperley-Lieb lattice models arising from quantum groups

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Quantum R matrix for G2 and a solvable 175-vertex model

. We show its natural origin from a thermodynamic Bethe ansatz analysis including chemical potentials.We propose a new

Analytic Bethe ansatz and T-system in C2(1) vertex models

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