Related papers: Solvable lattice models labelled by Dynkin diagram…
We introduce quantum dimer models on lattices made of corner-sharing triangles. These lattices includes the kagome lattice and can be defined in arbitrary geometry. They realize fully disordered and gapped dimer-liquid phase with…
For $n\in [-2,2]$ the $O(n)$ model on a random lattice has critical points to which a scaling behaviour characteristic of 2D gravity interacting with conformal matter fields with $c\in [-\infty,1]$ can be associated. Previously we have…
We prove that the sequence of the characters of the Kirillov-Reshetikhin (KR) modules $W_{m}^{(a)}, m\in \mathbb{Z}_{m\geq 0}$ associated to a node $a$ of the Dynkin diagram of a complex simple Lie algebra $\mathfrak{g}$ satisfies a linear…
The second $\mathbb{Z}_{3}$ parafermionic conformal theories are associated with the coset construction $\frac{SU(2)_{k}\times SU(2)_{4}}{SU(2)_{k+4}} $. Solid-on-solid integrable lattice models obtained by fusion of the model based on…
We introduce a family of comparative plausibility logics over neighbourhood models, generalising Lewis' comparative plausibility operator over sphere models. We provide axiom systems for the logics, and prove their soundness and…
We present the solution of a linear Restricted Solid--on--Solid (RSOS) model in a field. Aside from the origins of this model in the context of describing the phase boundary in a magnet, interest also comes from more recent work on the…
We consider the problem of constructing dense lattices of R^n with a given automorphism group. We exhibit a family of such lattices of density at least cn/2^n, which matches, up to a multiplicative constant, the best known density of a…
We describe varieties of minimal rational tangents on the wonderful symmetric varieties by marked Dynkin diagrams. An irreducible component of a variety of minimal rational tangents is a rational homogeneous space, and hence, we have a…
We initiate a new study on the correspondence between the 20-vertex model and a SOS (Solid-on-Solid) model. In comparison to two previous works of the author in 2024 which characterized properties of the transfer, and quantum monodromy,…
We analyse the problem of solving Boolean equation systems through the use of structure graphs. The latter are obtained through an elegant set of Plotkin-style deduction rules. Our main contribution is that we show that equation systems…
Zamolodchikov found an integrable field theory related to the Lie algebra E$_8$, which describes the scaling limit of the Ising model in a magnetic field. He conjectured that there also exist solvable lattice models based on E$_8$ in the…
We study a class of Labelled Oriented Graph (LOG) group where the underlying graph is a tadpole graph. We show that such a group is the natural HNN extension of a cyclically presented group and investigate the relationship between the LOG…
Applying Feynman diagrammatics to non-fermionic strongly correlated models with local constraints might seem generically impossible for two separate reasons: (i) the necessity to have a Gaussian (non-interacting) limit on top of which the…
This paper describes the use of simple lattice models for studying the properties of structurally disordered systems like glasses and granulates. The models considered have crystalline states as ground states, finite connectivity, and are…
The linked systems of symmetric group divisible designs of type II is introduced, and several examples are obtained from affine resolvable designs and mutually UFS Latin squares. Furthermore, an equivalence between such symmetric group…
A previous article was devoted to an analysis of the symmetry properties of a class of first-order delay ordinary differential systems (DODSs). Here we concentrate on linear DODSs. They have infinite-dimensional Lie point symmetry groups…
We develop an algebraic approach to solvable lattice models based on a chain of algebras obeyed by the models. In each subalgebra we use a unit, giving a chain of ideals. Thus, we divide the models into distinct sectors which do not mix.…
A lattice model of critical dense polymers is solved exactly for finite strips. The model is the first member of the principal series of the recently introduced logarithmic minimal models. The key to the solution is a functional equation in…
In this article we report a preliminary investigation of the large $N$ limit of a generalized one-matrix model which represents an $O(n)$ symmetric model on a random lattice. The model on a regular lattice is known to be critical only for…
For any Carter diagram $\Gamma$ containing 4-cycle, we introduce the partial Cartan matrix $B_L$, which is similar to the Cartan matrix associated with a Dynkin diagram. A linkage diagram is obtained from $\Gamma$ by adding one root…