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Related papers: Duality and Symmetry in Chiral Potts Model

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Method of derivation of the duality relations for two-dimensional Z(N)-symmetric spin models on finite square lattice wrapped on the torus is proposed. As example, exact duality relations for the nonhomogeneous Ising model (N=2) and the…

High Energy Physics - Theory · Physics 2008-02-03 A. I. Bugrij , V. N. Shadura

A closed-form exact analytical solution for the q-state Potts model on a ladder 2 x oo with arbitrary two-, three-, and four-site interactions in a unit cell is presented. Using the obtained solution it is shown that the finite-size…

Statistical Mechanics · Physics 2009-11-07 M. A. Yurishchev

The Kramers-Wannier duality introduces a well-known non-invertible symmetry in the critical transverse-field Ising model. In this work, we extend this concept to a broad class of quantum lattice models induced from integrability, providing…

High Energy Physics - Theory · Physics 2025-09-03 Rui-Dong Zhu

We establish explicit duality transformations for systems of M q-state Potts models coupled through their local energy density, generalising known results for M=1,2,3. The M-dimensional space of coupling constants contains a selfdual…

Statistical Mechanics · Physics 2016-08-31 Jesper Lykke Jacobsen

The $Z_N$-invariant chiral Potts model is considered as a perturbation of a $Z_N$ conformal field theory. In the self-dual case the renormalization group equations become simple, and yield critical exponents and anisotropic scaling which…

High Energy Physics - Theory · Physics 2009-10-22 John L. Cardy

We relate two classical dualities in low-dimensional quantum field theory: Kramers-Wannier duality of the Ising and related lattice models in $2$ dimensions, with electromagnetic duality for finite gauge theories in $3$ dimensions. The…

Algebraic Topology · Mathematics 2022-12-21 Daniel S. Freed , Constantin Teleman

We have found a simple criterion which allows for the straightforward determination of the order-disorder critical temperatures. The method reproduces exactly results known for the two dimensional Ising, Potts and $Z(N<5)$ models. It also…

High Energy Physics - Lattice · Physics 2009-10-22 J. Wosiek

We study the nonequilibrium dynamics of the $q$-state Potts model following a quench from the high temperature disordered phase to zero temperature. The time dependent two-point correlation functions of the order parameter field satisfy…

Condensed Matter · Physics 2009-10-28 Clement Sire , Satya N. Majumdar

We study the fate of the 2d kinetic q-state Potts model after a sudden quench to zero temperature. Both ground states and complicated static states are reached with non-zero probabilities. These outcomes resemble those found in the quench…

Statistical Mechanics · Physics 2014-01-03 J. Olejarz , P. L. Krapivsky , S. Redner

The Kramers-Wannier self-duality of critical quantum chains is examined from the perspective of model wave functions. We demonstrate, using the transverse-field Ising chain and the $3$-state Potts chain as examples, that the symmetry…

Statistical Mechanics · Physics 2025-05-23 Hua-Chen Zhang , Germán Sierra

A generalized gauge invariant Ising model on random surfaces with non-trivial topology is proposed and investigated with the dual transformation. It is proved that the model is self-dual in case of a self-dual lattice. In special cases the…

High Energy Physics - Theory · Physics 2009-09-25 Z. B. Li , B. Zheng , L. Schülke

We present a new solution of the asymmetric two-matrix model in the large $N$ limit which only involves a saddle point analysis. The model can be interpreted as Ising in the presence of a magnetic field, on random dynamical lattices with…

Statistical Mechanics · Physics 2007-05-23 P. Zinn-Justin

Starting with the Ising model, statistical models with global symmetries provide fruitful approaches to interesting physical systems, for example percolation or polymers. These include the $O(n)$ model (symmetry group $O(n)$) and the Potts…

High Energy Physics - Theory · Physics 2025-01-29 Paul Roux , Jesper Lykke Jacobsen , Sylvain Ribault , Hubert Saleur

This paper rests to a large extend on a paper I wrote some time ago on 'Duality in generalized Ising models and phase transitions without local order parameter'. It deals with Ising models with interactions containing products of more than…

High Energy Physics - Lattice · Physics 2014-11-24 Franz J. Wegner

The ferromagnetic q-state Potts model on a square lattice is analyzed, for q>4, through an elaborate version of the operatorial variational method. In the variational approach proposed in the paper, the duality relations are exactly…

Statistical Mechanics · Physics 2009-10-30 L. Angelini , M. Pellicoro , I. Sardella , M. Villani

The spontaneous magnetization of a two-dimensional lattice model can be expressed in terms of the partition function $W$ of a system with fixed boundary spins and an extra weight dependent on the value of a particular central spin. For the…

Statistical Mechanics · Physics 2015-05-13 R. J. Baxter

The Wegner $Z_2$ gauge theory-$Z_2$ Ising spin model duality in $(2+1)$ dimensions is revisited and derived through a series of canonical transformations. The Kramers-Wannier duality is similarly obtained. The Wegner $Z_2$ gauge-spin…

High Energy Physics - Lattice · Physics 2016-11-21 Manu Mathur , T. P. Sreeraj

We establish a direct link between massive Ising model and arbitrary massive $N=2$ supersymmetric QFT's in two dimensions. This explains why the equations which appear in the computation of spin-correlations in the non-critical Ising model…

High Energy Physics - Theory · Physics 2009-10-22 S. Cecotti , C. Vafa

The Onsager algebra, invented to solve the two-dimensional Ising model, can be used to construct conserved charges for a family of integrable $N$-state chiral clock models. We show how it naturally gives rise to a "pivot" procedure for this…

Statistical Mechanics · Physics 2025-03-19 Nick G. Jones , Abhishodh Prakash , Paul Fendley

In various statistical-mechanical models the introduction of a metric onto the space of parameters (e.g. the temperature variable, $\beta$, and the external field variable, $h$, in the case of spin models) gives an alternative perspective…

Statistical Mechanics · Physics 2008-11-26 B. P. Dolan , D. A. Johnston , R. Kenna