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Item type: Publication , Access status: Metadata only , Partition function of a three-dimensional solvable model(1993-03-15) Bazhanov, V. V.; Baxter, R. J.The solvable generalized chiral Potts model can be interpreted as a three-dimensional lattice model with local interactions. To within a minor modification of the boundary conditions it is an Ising type model with the specific two- and three-spin interactions on the body centered cubic lattice. Here we report the results of a calculation of the partition function per site for the infinite lattice.Item type: Publication , Access status: Metadata only , New solvable lattice models in three dimensions(1992) Bazhanov, V. V.; Baxter, R. J.In this paper we establish a remarkable connection between two seemingly unrelated topics in the area of solvable lattice models. The first is the Zamolodchikov model, which is the only nontrivial model on a three-dimen-sional lattice so far solved. The second is the chiral Potts model on the square lattice and its generalization associated with the Uq(sl(n)) algebra, which is of current interest due to its connections with high-genus algebraic curves and with representations of quantum groups at roots of unity. We show that this last "sl(n)-generalized chiral Potts model" can be interpreted as a model on a threedimensional simple cubic lattice consisting of n square-lattice layers with an N- valued (N≥2) spin at each site. Further, in the N=2 case this three-dimen-sional model reduces (after a modification of the boundary conditions) to the Zamolodchikov model we mentioned above.Item type: Publication , Access status: Metadata only , Quantum field theories in finite volume: Excited state energies(1997-04-07) Bazhanov, Vladimir V.; Lukyanov, Sergei L.; Zamolodchikov, Alexander B.We develop a method of computing the excited state energies in Integrable Quantum Field Theories (IQFT) in finite geometry, with the spatial coordinate compactified on a circle of circumference R. The IQFT "commuting transfer matrices" introduced earlier [Commun. Math. Phys. 177 (1996) 381] for Conformal Field Theories (CFT) are generalized to non-conformal IQFT obtained by perturbing CFT with the operator Φ1.3. We study the models in which the fusion relations for these "transfer matrices" truncate and provide closed integral equations which generalize the equations of the thermodynamic Bethe ansatz to excited states. The explicit calculations are done for the first excited state in the "scaling Lee-Yang model".Item type: Publication , Access status: Metadata only , Remarks on the quantum dilogarithm(1995) Bazhanov, V. V.; Reshetikhin, N. YuA quantum analogue of the dilogarithm function has been introduced by Faddeev and Kashaev (1994) in such a way that a certain identity in the Weyl algebra Wq, plays the role of the five-term dilogarithm identity. We study this identity in the limit when q approaches a root of unity and show that it then reduces to the 'restricted star-triangle relation' which has been used previously by Bazhanov and Baxter (1992) as a local integrability condition of a class of three-dimensional solvable lattice models.Item type: Publication , Access status: Metadata only , Numerical results for the three-state critical Potts model on finite rectangular lattices(1995) O'Rourke, M. J.; Baxter, R. J.; Bazhanov, V. V.Partition functions for the three-state critical Potts model on finite square lattices and for a variety of boundary conditions are presented. The distribution of their zeros in the complex plane of the spectral variable is examined and is compared to the expected infinite-lattice result. The partition functions are then used to test the finite-size scaling predictions of conformal and modular invariance.