The two-dimensional q-state Potts model is subjected to a Z(q) symmetric disorder that allows for the existence of a Nishimori line. At q=2, this model coincides with the +/- J random-bond Ising model. For q>2, apart from the usual pure- and zero-temperature fixed points, the ferro/paramagnetic phase boundary is controlled by two critical fixed points: a weak disorder point, whose universality ...

We consider the q-state Potts spin-glass model, with quenched couplings taking two different values only. As an approximation for this model a proper generalization of the random energy model is derived. Formulas of the resulting diluted generalized random energy model (DGREM) are applied to calculate the ground-state energy for the two-dimensional Potts spin-glass model. The semianalytical res...

We use the Density Matrix Renormalization Group technique to compute correlation functions of the Z3-chiral Potts quantum chain in the massive regimes. Chains of up to 70 sites are used and a clear oscillatory behavior is found. We also check the relation between the density matrix spectrum and the Corner Transfer Matrix spectrum pointed out by Nishino and Okunishi, using Baxter’s low-temperatu...

in this paper, i present additional information for policy-makers and researchers to consider in response to the view proposed by potts et al that “the pill is mightier than the sword.” i identify states with both high rates of terrorism and a youth bulge and discuss correlates of both these societal characteristics. the research examined supports the view that factors other than access to fami...

We discuss the q-state Potts models for q ≤ 4, in the scaling regimes close to their critical or tricritical points. Starting from the kink S-matrix elements proposed by Chim and Zamolodchikov, the bootstrap is closed for the scaling regions of all critical points, and for the tricritical points when 4 > q ≥ 2. We also note a curious appearance of the extended last line of Freudenthal’s magic s...

Weconsider the Pottsmodelwith q colors on a sequence ofweighted graphs with adjacency matrices An , allowing for both positive and negative weights. Under a mild regularity condition on An we show that the mean-field prediction for the log partition function is asymptotically correct, whenever tr(An) = o(n). In particular, our results are applicable for the Ising and the Potts models on any seq...

We consider the fractal dimensions of critical clusters occurring in configurations of a q-state Potts model coupled to the planar random graphs of the dynamical triangulations approach to Euclidean quantum gravity in two dimensions. For regular lattices, it is well-established that at criticality the properties of Fortuin–Kasteleyn clusters are directly related to the conventional critical exp...

We propose an effective framework for multi-phase image segmentation and semi-supervised data clustering by introducing a novel region force term into the Potts model. Assume the probability that a pixel or a data point belongs to each class is known a priori. We show that the corresponding indicator function obeys the Bernoulli distribution and the new region force function can be computed as ...

The q-state Potts model can be defined on an arbitrary finite graph, and its partition function encodes much important information about that graph, including its chromatic polynomial, flow polynomial and reliability polynomial. The complex zeros of the Potts partition function are of interest both to statistical mechanicians and to combinatorists. I give a pedagogical introduction to all these...

The chiral Potts model is a generalization of the N -state Potts model allowing for handedness of the pair interactions. While known under several other names, it has received much interest in the past two decades. It may have appeared first in a short paper by Wu and Wang in the context of duality transformations. However, active studies of chiral Potts models did not start until a few years a...