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Three-state anti-ferromagnetic Potts model in three dimensions: universality and critical amplitudes

Aloysius P. Gottlob, Martin Hasenbusch B

arXiv:cond-mat/9404087Physica A Statistical Mechanics and its ApplicationsSep 1, 199425 citations

Critical behaviour in three-state Potts antiferromagnets on a Bethe lattice

Fulvio Peruggi, Francesco di Liberto, Gabriella Monroy

Physica A Statistical Mechanics and its ApplicationsMay 1, 198514 citations

Anyonic Interpretation of Virasoro Characters and the Thermodynamic Bethe Ansatz

Berlin Sfb Preprint, A. G. Bytsko, A. Fring

Employing factorized versions of characters as products of quantum dilogarithms corresponding to irreducible representations of the Virasoro algebra, we obtain character formulae which admit an anyonic quasi-particle interpretation in the context of minimal models in conformal field theories. We propose anyonic thermodynamic Bethe ansatz equations, together with their corresponding equation for the Virasoro central charge, on the base of an analysis of the classical limit for the characters and the requirement that the scattering matrices are asymptotically phaseless.Employing factorized versions of characters as products of quantum dilogarithms corresponding to irreducible representations of the Virasoro algebra, we obtain character formulae which admit an anyonic quasi-particle interpretation in the context of minimal models in conformal field theories. We propose anyonic thermodynamic Bethe ansatz equations, together with their corresponding equation for the Virasoro central charge, on the base of an analysis of the classical limit for the characters and the requirement that the scattering matrices are asymptotically phaseless.

Jan 1, 19978 citations

The magnetic critical exponent in the three-state three-dimensional Potts model

Massimo Bernaschi, Luca Biferale, L. A. Fernández +3 more

Physics Letters BApr 1, 19903 citations

The off-critical integrable Ashkin-Teller model

Paul A. Pearce, Katherine Seaton

The exact solution of an Ashkin-Teller model, with layer and spatial anisotropy and Z 2 *Z 2 symmetry, is presented. The model is related to the eight-vertex model by a sublattice or orbifold duality and it has the same free energy and magnetisation. The exact solution manifold is a three-dimensional submanifold of the full six-dimensional thermodynamic space. It admits a Z 3 symmetry relating three regimes each exhibiting different partial order. In the spatially isotropic case, these regimes are separated by three lines of continuously varying critical behaviour which coalesce at the four-state Potts critical point. The magnetisations and polarisation are derived using corner transfer matrices giving rise to the appearance of chiral and Virasoro characters. The associated critical exponents confirm the known values. In particular, one obtains the value x sigma =1/8 for the magnetic scaling dimension and identify the next-to-leading thermal field.The exact solution of an Ashkin-Teller model, with layer and spatial anisotropy and Z 2 *Z 2 symmetry, is presented. The model is related to the eight-vertex model by a sublattice or orbifold duality and it has the same free energy and magnetisation. The exact solution manifold is a three-dimensional submanifold of the full six-dimensional thermodynamic space. It admits a Z 3 symmetry relating three regimes each exhibiting different partial order. In the spatially isotropic case, these regimes are separated by three lines of continuously varying critical behaviour which coalesce at the four-state Potts critical point. The magnetisations and polarisation are derived using corner transfer matrices giving rise to the appearance of chiral and Virasoro characters. The associated critical exponents confirm the known values. In particular, one obtains the value x sigma =1/8 for the magnetic scaling dimension and identify the next-to-leading thermal field.

Journal of Physics A Mathematical and GeneralApr 7, 19906 citations

Three-state Potts model on the maple leaf lattice

Z. F. Wang, B. W. Southern

We use Monte Carlo methods to study the three-state Potts model on a two-dimensional lattice with fivefold coordination. The lattice consists of triangular and hexagonal units and has properties intermediate between the triangular and kagom\'e lattices. The critical behavior of both ferromagnetic and antiferromagnetic cases is considered. As expected, the critical behavior of the ferromagnetic model is independent of the lattice details and lies in the universality class of the three-state ferromagnetic Potts model. A critical end point is found at the coexistence between the ferromagnetic and antiferromagnetic phases, and the transition to the antiferromagnetic state is always first order.We use Monte Carlo methods to study the three-state Potts model on a two-dimensional lattice with fivefold coordination. The lattice consists of triangular and hexagonal units and has properties intermediate between the triangular and kagom\'e lattices. The critical behavior of both ferromagnetic and antiferromagnetic cases is considered. As expected, the critical behavior of the ferromagnetic model is independent of the lattice details and lies in the universality class of the three-state ferromagnetic Potts model. A critical end point is found at the coexistence between the ferromagnetic and antiferromagnetic phases, and the transition to the antiferromagnetic state is always first order.

Physical review. B, Condensed matterSep 18, 20037 citations

Virasoro characters from bethe equations for the critical ferromagnetic three-state potts model

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