We discover a Ising-type duality in the general N -state chiral Potts model, which is the Kramers-Wannier duality of planar Ising model when N = 2. This duality relates the spectrum and eigenvectors of one chiral Potts model at a low temperature (of small k) to those of another chiral Potts model at a high temperature (of k). The τ -model and chiral Potts model on the dual lattice are establish...

We investigate the nonsmooth and nonconvex L1-Potts functional in discrete and continuous time. We show Γ-convergence of discrete L1-Potts functionals toward their continuous counterpart and obtain a convergence statement for the corresponding minimizers as the discretization gets finer. For the discrete L1-Potts problem, we introduce an O(n2) time and O(n) space algorithm to compute an exact m...

We study in this paper the phase transition in a mobile Potts model by the use of Monte Carlo simulation. The mobile Potts model is related to a diluted Potts model, which is also studied here by a mean-field approximation. We consider a lattice where each site is either vacant or occupied by a q-state Potts spin. The Potts spin can move from one site to a nearby vacant site. In order to study ...

In this paper, we present a fast numerical scheme to estimate Partition Functions (PF) of symmetric Potts fields. Our strategy is first validated on 2D two-color Potts fields and then on 3D twoand three-color Potts fields. It is then applied to the joint detection-estimation of brain activity from functional Magnetic Resonance Imaging (fMRI) data, where the goal is to automatically recover acti...

The q-state chiral Potts model can describe systems that exhibit rich phase diagrams (see, for instance, ref. [l]) and interesting physical properties like commensurate-incommensurate transitions [2]. The chiral Potts model has been extensively studied in the last few years from the point of view of exactly solvable models. Au-Yang et al. discovered integrable cases for the q-state chiral Potts...

We discuss generalizations of the Temperley-Lieb algebra in the Potts and XXZ models. These can be used to describe the addition of different types of integrable boundary terms. We use the Temperley-Lieb algebra and its one-boundary, two-boundary, and periodic extensions to classify different integrable boundary terms in the 2, 3, and 4-state Potts models. The representations always lie at crit...

We establish the Bethe equation of the τ -model in the N -state chiral Potts model (including the degenerate selfdual 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 degener...

We report on single-cluster Monte Carlo simulations of the Ising, 4-state Potts and 10-state Potts models on quenched ensembles of planar, tri-valent (Φ3) random graphs. We confirm that the firstorder phase transition of the 10-state Potts model on regular 2D lattices is softened by the quenched connectivity disorder represented by the random graphs and that the exponents of the Ising and 4stat...

The Zipf power law and its connection with the inhomogeneity of the system is investigated. We describe the statistical distributions of the domain masses in the Potts model near the temperature-induced phase transition. We found that the statistical distribution near the critical point is described by the power law form with a long tail, while beyond the critical point the power law tail is su...