OBJECTIVES Palliative Potts shunt has been proposed in children with suprasystemic pulmonary arterial hypertension (PAH). METHODS A retrospective multicentre study was performed to assess short- and long-term outcomes after Potts shunt. RESULTS From 2003 to 2014, 24 children underwent a Potts shunt [19 surgical, median age: 7.7 years (1.5-17 years), median weight: 19.5 kg (10.2-47 kg) and 5...

We demonstrate that the τ (j)-matrices in the superintegrable chiral Potts model possess the Onsager algebra symmetry for their degenerate eigenvalues. The Fabricius-McCoy comparison of functional relations of eight-vertex model for roots of unity and superintegrable chiral Potts model has been carefully analyzed by identifying equivalent terms in the corresponding equations , by which we extra...

Here we observe that list coloring in graph theory coincides with the zero-temperature antiferromagnetic Potts model with an external field. We give a list coloring polynomial that equals the partition function in this case. This is analogous to the well-know connection between the chromatic polynomial and the zero-temperature, zero-field, antiferromagnetic Potts model. The subsequent cross fer...

We examine the order of the phase transition in the Potts model by using the graph representation for the partition function, which allows treating a non-integer number of Potts states. The order of transition is determined by the analysis of the shape of the graph-weight probability distribution. The approach is illustrated on special cases of the one-dimensional Potts model with long-range in...

It has been known for some time that the Boltzmann weights of the chiral Potts model can be parametrized in terms of hyperelliptic functions, but as yet no such parametrization has been applied to the partition and correlation functions. Here we show that for N = 3 the function S(t p) that occurs in the recent calculation of the order parameters can be expressed quite simply in terms of such a ...

We study Gibbs properties of the fuzzy Potts model in the mean field case (i.e. on a complete graph) and on trees. For the mean field case, a complete characterization of the set of temperatures for which non-Gibbsianness happens is given. The results for trees are somewhat less explicit, but we do show for general trees that nonGibbsianness of the fuzzy Potts model happens exactly for those te...

We consider the perturbations of the 3-state Potts conformal field theory introduced by Cardy as a description of the chiral 3-state Potts model. By generalising Zamolodchikov's counting argument and by explicit calculation we find new inhomogeneous conserved currents for this theory. We conjecture the existence of an infinite set of conserved currents of this form and discuss their relevance t...

Abstract The renormalization group method has been developed to investigate p -adic q -state Potts models on the Cayley tree of order k . This is closely related examination dynamical behavior Potts–Bethe mapping which depends parameters , In Mukhamedov and Khakimov [Chaotic Potts–Behte mapping. Discrete Contin. Dyn. Syst. 38 (2018), 231–245], we have considered case when not divisible by and, ...

Ganikhodjaev and Razak have proved versions of the two Griffiths inequalities for the ferromagnetic Potts model. We show how their inequalities may be derived via the FKG inequality for the random-cluster representation of the Potts model.