Related papers: Towards integrable structure in 3d Ising model
In the framework of the Poisson geometry of twistor space we consider a family of perturbed 3-dimensional Kepler systems. We show that Hamilton equations of this systems are integrated by quadratures. Their solutions for some subcases are…
Soibelman's theory of quantized function algebra A_q(SL_n) provides a representation theoretical scheme to construct a solution of the Zamolodchikov tetrahedron equation. We extend this idea originally due to Kapranov and Voevodsky to…
Fusion hierarchies of \ade face models are constructed. The fused critical $D$, $E$ and elliptic $D$ models yield new solutions of the Yang-Baxter equations with bond variables on the edges of faces in addition to the spin variables on the…
We analytically derive the geometrical structure of the weight space in multilayer neural networks (MLN), in terms of the volumes of couplings associated to the internal representations of the training set. Focusing on the parity and…
By means of toric geometry we study hypersurfaces in weighted projective space of dimension four. In particular we compute for a given manifold its intrinsic topological coupling. We find that the result agrees with the calculation of the…
A multiparametric extension of the anisotropic U model is discussed which maintains integrability. The R-matrix solving the Yang-Baxter equation is obtained through a twisting construction applied to the underlying Uq(sl(2|1))…
Recently, the first-named author gave a classification of 3D consistent 6-tuples of quad-equations with the tetrahedron property; several novel asymmetric 6-tuples have been found. Due to 3D consistency, these 6-tuples can be extended to…
Using a Poisson bracket representation, in 3D, of the Lie algebra $\mathfrak{sl}(2)$, we first use highest weight representations to embed this into larger Lie algebras. These are then interpreted as symmetry and conformal symmetry algebras…
We present examples in three symmetry classes of topological insulators in one or two dimensions where the proof of the bulk-edge correspondence is particularly simple. This serves to illustrate the mechanism behind the bulk-edge principle…
Matrix models with continuous symmetry are powerful tools for studying quantum gravity and holography. Tensor models have also found applications in holographic quantum gravity. Matrix models with discrete permutation symmetry have been…
In this paper, we apply the hierarchical modeling technique and study some numerical linear algebra problems arising from the Brownian dynamics simulations of biomolecular systems where molecules are modeled as ensembles of rigid bodies.…
Exploring a mapping among $n$-state spin and vertex models on the square lattice we argue that a given integrable spin model with edge weights satisfying the rapidity difference property can be formulated in the framework of an equivalent…
We study solutions of the reflection equation related to the quantum affine algebra $U_q(\widehat{sl_n})$. First, we explain how to construct a family of stochastic integrable vertex models with fixed boundary conditions. Then, we construct…
We consider a special class of quantum non-dynamical $R$-matrices in the fundamental representation of ${\rm GL}_N$ with spectral parameter given by trigonometric solutions of the associative Yang-Baxter equation. In the simplest case $N=2$…
The three-dimensional (3D) Ising model is mapped into a 3D spinless fermionic model by the Jordan-Wigner transformation. The exact solution of the 3D model for spinless fermions is derived analytically by performing a diagonalization…
This paper is devoted to tetrahedron maps, which are set-theoretical solutions to the Zamolodchikov tetrahedron equation. We construct a family of tetrahedron maps on associative rings. We show that matrix tetrahedron maps presented in…
We note that two formulations of dual gonihedric Ising models in 3d, one based on using Wegner's general framework for duality to construct a dual Hamiltonian for codimension one surfaces, the other on constructing a dual Hamiltonian for…
A new integrable model which is a variant of the one-dimensional Hubbard model is proposed. The integrability of the model is verified by presenting the associated quantum R-matrix which satisfies the Yang-Baxter equation. We argue that the…
In all structural models, the section or fiber response is a relation between the strain measures and the stress resultants. This relation can only be expressed in a simple analytical form when the material response is linear elastic. For…
We prove that the number of 3-dimensional simplicial complexes having the spherical topology grows exponentially as a function of a volume. It is suggested that the 3d simplicial quantum gravity has qualitatively the same phase structure as…