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Self-dual renormalization group analysis of the Potts models

D. Horn, Marek Karliner A, Shimon Yankielowicz B

Nuclear Physics BDec 1, 198013 citations

Microcanonical transfer matrix study of the Q-state Potts model

Richard J. Creswick, Seung‐Yeon Kim

arXiv:cond-mat/9810153Computer Physics CommunicationsSep 1, 199911 citations

Bethe equation of the τ(2)model and eigenvalues of a finite-size transfer matrix of a chiral Potts model with alternating rapidities

Shi-shyr Roan

We establish the Bethe equation of the τ (2) model in the N -state chiral Potts model (including the degenerate self-dual 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 degeneracy of the τ (2) model found as in the homogeneous superintegrable chiral Potts model.

arXiv:0805.1585Journal of Statistical Mechanics Theory and ExperimentOct 1, 20085 citations

Renormalization group study of the three state three dimensional potts model

Massimo Bernaschi

Nuclear Physics B - Proceedings SupplementsSep 1, 19901 citation

Self-dual D-dimensional quantum Potts model with multi-spin interactions

Loïc Turban

Introduces a family of D-dimensional q-state quantum Potts models with multi-spin interactions, which are self-dual for any D. These models are introduced using their (d=D+1)-dimensional classical formulations and the transfer matrix technique. The self-duality is proved on the quantum Hamiltonian. In the limit q to infinity the ground state energy is obtained exactly and the phase transition is first-order. A 1/q expansion allows one to get an approximate expression for the line in the (q,D)-plane separating regions where the transition changes from first- to second-order.Introduces a family of D-dimensional q-state quantum Potts models with multi-spin interactions, which are self-dual for any D. These models are introduced using their (d=D+1)-dimensional classical formulations and the transfer matrix technique. The self-duality is proved on the quantum Hamiltonian. In the limit q to infinity the ground state energy is obtained exactly and the phase transition is first-order. A 1/q expansion allows one to get an approximate expression for the line in the (q,D)-plane separating regions where the transition changes from first- to second-order.

Journal of Physics A Mathematical and GeneralMay 1, 19820 citations

Duality relations for M coupled Potts models

Jesper Lykke Jacobsen

We establish explicit duality transformations for systems of M q-state Potts models coupled through their local energy density, generalizing known results for M=1,2,3. The M-dimensional space of coupling constants contains a self-dual submanifold of dimension D(M)=[M/2]. For the case M=4, the variation of the effective central charge along the self-dual surface is investigated by numerical transfer matrix techniques. Evidence is given for the existence of a family of critical points, corresponding to conformal field theories with an extended S(M) symmetry algebra.We establish explicit duality transformations for systems of M q-state Potts models coupled through their local energy density, generalizing known results for M=1,2,3. The M-dimensional space of coupling constants contains a self-dual submanifold of dimension D(M)=[M/2]. For the case M=4, the variation of the effective central charge along the self-dual surface is investigated by numerical transfer matrix techniques. Evidence is given for the existence of a family of critical points, corresponding to conformal field theories with an extended S(M) symmetry algebra.

Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topicsJul 1, 200033 citations

Self-dual transfer matrix renormalization for the triangular Potts model

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