From rarefied elliptic beta integral to parafermionic star-triangle relation

Star - Triangle Relation for a Three Dimensional Model

The solvable sl(n)-chiral Potts model can be interpreted as a three-dimensional lattice model with local interactions. To within a minor modification of the boundary conditions it is an Ising type model on the body centered cubic lattice with twoand threespin interactions. The corresponding local Boltzmann weights obey a number of simple relations, including a restricted star-triangle relation,...

from historical facts to geo-political realities: relation between turkey and armenia ( 1915 – 2010)

armenias geopolitics and its historical experience have had a determining impact on the character of its foreign policy .present-day armenia is a small, landlocked country with _11,620 square miles area armenias landlocked nature makes it dependent on the benevolence of its neighbors for access to the outside world a fact that gives it a sense of isolation and vulnerability. as it was indic...

Graphical Approach to the Nonintersecting String Model: Star-triangle Equation, Inversion Relation, and Exact Solution

A general q-state nonintersecting string model for q Z 2 is studied, and solved, using a graphical approach. This model, of which special cases were first introduced by Stroganov and Schultz, has recently drawn further attention because of its relation to Potts models. In its simplest version, a uniform, separable nonintersecting string model on a quadratic lattice, it corresponds to a q*-state...

Star – triangle equivalence in soap froths

In two dimensional foams at equilibrium, triangular bubbles can be freely exchanged with 3-fold stars —three edges ending at a central vertex. This theorem is deduced here from Moukarzel’s duality. Moreover, to probe the method, a few related properties are established: under slow gas diffusion, T2 processes are continuous for triangles but not for other types of bubbles. In general, the gas fl...

From Reconstructive Triangle to Reconstructive Quadrangle: Time to Include Tissue Distraction in the Reconstructive Algorithms