Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:cond-mat/9812227 · Nuclear Physics B

Coupled Potts models: Self-duality and fixed point structure

Vladimir S. Dotsenko, Jesper Lykke Jacobsen, Marc-André Lewis, Marco Picco

Published May 1, 1999• 46 citations
arXivHTMLPDF
DOI
10.1016/s0550-3213(99)00097-8

Related papers

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.

Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics•Jul 1, 2000•33 citations

Universality of coupled Potts models

Vladimir S. Dotsenko, Jesper Lykke Jacobsen, Xuan Son Nguyen +1 more

arXiv:cond-mat/0112120•Nuclear Physics B•Jun 1, 2002•6 citations

Scaling in the vicinity of the four-state Potts fixed point

Henk W. J. Blöte, Wenan Guo, M. P. Nightingale

Abstract We study a self-dual generalization of the Baxter–Wu model, employing results obtained by transfer matrix calculations of the magnetic scaling dimension and the free energy. While the pure critical Baxter–Wu model displays the critical behavior of the four-state Potts fixed point in two dimensions, in the sense that logarithmic corrections are absent, the introduction of different couplings in the up- and down triangles moves the model away from this fixed point, so that logarithmic corrections appear. Real couplings move the model into the first-order range, away from the behavior displayed by the nearest-neighbor, four-state Potts model. We also use complex couplings, which bring the model in the opposite direction characterized by the same type of logarithmic corrections as present in the four-state Potts model. Our finite-size analysis confirms in detail the existing renormalization theory describing the immediate vicinity of the four-state Potts fixed point.

arXiv:1710.06088•Journal of Physics A Mathematical and Theoretical•Jun 23, 2017•6 citations

Potts transition in coupled XY models

Victor Drouin-Touchette, Peter P. Orth, Premala Chandra +2 more

Bulletin of the American Physical Society•Mar 6, 2019•0 citations

Coupled critical models: application to Ising-Potts models

Pascal Simon

arXiv:cond-mat/9705292•Physics Letters B•Sep 1, 1997•3 citations

An Energy Curve Family of a Semi-Infinite Lattice and the Transition Point in the Potts Model

Hiroshi Katsumori, Shingo Ohya

An energy curve family for a semi-infinite square lattice (l × ∞) of the q-state Potts model with periodic boundary conditions has an l-independent common fixed point, which gives the exact critical values of the coupling parameter K = J/kJ and the internal energy E(K), as a natural consequence of the self-dual property of the model. An energy curve intersection procedure (ECIP) is proposed to find the critical properties of the Potts model through numerical investigation of the transfer matrix. The ECIP shows that the lattices (l × ∞) for two different small values of l can reproduce the transition temperature and the critical internal energy of the bulk lattice (∞ × ∞) without use of the duality argument. As an applicable example of the ECIP, a semi-infinite simple cubic lattice (l × m × ∞) of the Potts model is preliminarily studied to obtain approximate critical quantities of the layer lattice (l × ∞ × ∞). A brief comment on the specific heat exponent μ estimated using the ECIP is added.

Progress of Theoretical Physics•Jun 1, 2000•0 citations
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.
Abstract We study a self-dual generalization of the Baxter–Wu model, employing results obtained by transfer matrix calculations of the magnetic scaling dimension and the free energy. While the pure critical Baxter–Wu model displays the critical behavior of the four-state Potts fixed point in two dimensions, in the sense that logarithmic corrections are absent, the introduction of different couplings in the up- and down triangles moves the model away from this fixed point, so that logarithmic corrections appear. Real couplings move the model into the first-order range, away from the behavior displayed by the nearest-neighbor, four-state Potts model. We also use complex couplings, which bring the model in the opposite direction characterized by the same type of logarithmic corrections as present in the four-state Potts model. Our finite-size analysis confirms in detail the existing renormalization theory describing the immediate vicinity of the four-state Potts fixed point.
An energy curve family for a semi-infinite square lattice (l × ∞) of the q-state Potts model with periodic boundary conditions has an l-independent common fixed point, which gives the exact critical values of the coupling parameter K = J/kJ and the internal energy E(K), as a natural consequence of the self-dual property of the model. An energy curve intersection procedure (ECIP) is proposed to find the critical properties of the Potts model through numerical investigation of the transfer matrix. The ECIP shows that the lattices (l × ∞) for two different small values of l can reproduce the transition temperature and the critical internal energy of the bulk lattice (∞ × ∞) without use of the duality argument. As an applicable example of the ECIP, a semi-infinite simple cubic lattice (l × m × ∞) of the Potts model is preliminarily studied to obtain approximate critical quantities of the layer lattice (l × ∞ × ∞). A brief comment on the specific heat exponent μ estimated using the ECIP is added.