We study nonequilibrium steady states of a one-dimensional stochastic model, originally introduced as an approximation the Discrete Nonlinear Schr\"odinger equation. This model is characterized by two conserved quantities, namely mass and energy; it displays ``normal", homogeneous phase, separated condensed (negative-temperature) where macroscopic fraction energy localized on single lattice sit...

The action of the symmetric group S4 on the Tetrahedron algebra, introduced by Hartwig and Terwilliger [HT05], is studied. This action gives a grading of the algebra which is related to its decomposition in [HT05] into a direct sum of three subalgebras isomorphic to the Onsager algebra. The ideals of both the Tetrahedron algebra and the Onsager algebra are determined.

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...

1 Definition and the basic properties The Ising model (IM) was invented by Lenz. His student Ising has found the partition function of the 1d model and tried to solve 2d model but failed. The exact solution of 2d model was found by Onsager in 1942-1944. It is one of the fundamental results in statistical physics. The IM consist of spins σ x = ±1 ascribed to sites of a lattice x. The energy of ...

where β = q+q and δ = −(q − q) 2 . (TD) can be regarded as a q-analogue of the DolanGrady relations and we call A the q-Onsager algebra. We classify the finite-dimensional irreducible representations of A. All such representations are explicitly constructed via embeddings of A into the Uq(sl2)-loop algebra. As an application, tridiagonal pairs of qRacah type over C are classified in the case wh...

In this paper we will establish formulas for the correlations of the two-dimensional Ising model in the absence of a magnetic field and prove the convergence of the scaling limit from above and below the critical temperature. The theoretical developments which lead up to our results begin with Onsager’s calculation of the free energy for this model in a classic 1944 paper [52). Statistical mech...