Related papers: Discrete Holomorphic Parafermions in the Eight Ver…
We extend an operator formalism, developed by Hongler, Kyt\"ol\"a, and Zahabi in 2012 for the Ising model, to the Ashkin-Teller and loop $\mathrm{O} ( n ) $ models. The formalism is primarily dependent upon notions of massive, and massless,…
We find discrete holomorphic parafermions of the Ashkin-Teller model on the critical line, by mapping appropriate interfaces of the model to the $O(n=1)$ model. We give support to the conjecture that the curve created by the insertion of…
We define parafermionic observables in various lattice loop models, including examples where no Kramers-Wannier duality holds. For a particular rhombic embedding of the lattice in the plane and a value of the parafermionic spin these…
We construct lattice parafermions - local products of order and disorder operators - in nearest-neighbor Z(N) models on regular isotropic planar lattices, and show that they are discretely holomorphic, that is they satisfy discrete…
We propose that the correlation functions of the inhomogeneous eight vertex model in the anti-ferroelectric regime satisfy a system of difference equations with respect to the spectral parameters. Solving the simplest difference equation we…
We consider several anisotropic extensions of the Belavin model, and show that integrability holds also for the massive case for some specific relations between the coupling constants. This is done by relating the S-matrix factorization…
We initiate a study of the classification of approximation complexity of the eight-vertex model defined over 4-regular graphs. The eight-vertex model, together with its special case the six-vertex model, is one of the most extensively…
The inhomogeneous six-vertex model is a 2$D$ multiparametric integrable statistical system. In the scaling limit it is expected to cover different classes of critical behaviour which, for the most part, have remained unexplored. For general…
An integrable eight state supersymmtric $U$ model is proposed, which is a fermion model with correlated single-particle and pair hoppings as well as uncorrelated triple-particle hopping. It has an $gl(3|1)$ supersymmetry and contains one…
It is widely believed that the critical properties of several planar lattice models, like the Eight Vertex or the Ashkin-Teller models, are well described by an effective Quantum Field Theory obtained as formal scaling limit. On the basis…
The discovery of fracton states of matter opens up an exciting, largely unexplored field of many-body physics. Certain fracton states' similarity to gravity is an intriguing property. In an earlier work [H. Yan, Phys. Rev. B 99, 155126…
Whereas the tools to determine the eigenvalues of the eight-vertex transfer matrix T are well known there has been until recently incomplete knowledge about the eigenvectors of T. We describe the construction of eigenvectors of T…
We show that the single-mode parafermionic type systems possess supersymmetry, which is based on the symmetry of characteristic functions of the parafermions related to the generalized deformed oscillator of Daskaloyannis et al. The…
The eight-vertex model at the reflectionless points is considered on the basis of Smirnov's axiomatic approach. Integral formulae for form factors of the eight-vertex model can be obtained in terms of those of the eight-vertex SOS model, by…
In this note we study `a la Baxter [1] the possible integrable manifolds of the asymmetric eight-vertex model. As expected they occur when the Boltzmann weights are either symmetric or satisfy the free-fermion condition but our analysis…
We have briefly analyzed the existence of the pseudofermionic structure of multilevel pseudo-Hermitian systems with odd time-reversal and higher order involutive symmetries. We have shown that 2N-level Hamiltonians with N-order eigenvalue…
We study a generalized 8-vertex model where the vertices are coupled to a locally varying field. We rewrite the partition function as an integral over Grassmann variables. In this form it is possible to explicitly evaluate all terms of the…
We review the recently discovered symmetries of the 8 and 6 vertex models which exist at roots of unity and present their relation with representation theory of affine Lie algebras, Drinfeld polynomials and Bethe vectors.
The A-model for finite rank singular perturbations of class $\mathfrak{H}_{-m-2}\smallsetminus\mathfrak{H}_{-m-1}$, $m\in\mathbb{N}$, is considered from the perspective of boundary relations. Assuming further that the Hilbert spaces…
This note gives a uniform, self-contained, and fairly direct approach to a variety of obstruction-theoretic problems on 8-manifolds. We give necessary and sufficient cohomological critera for the existence of almost complex and almost…