38 citations · 265 across the 20 of their papers we have counts for
20 papers
Quasi-classical expansion of a hyperbolic solution to the star-star relation and multicomponent 5-point difference equations
Andrew P. Kels
The quasi-classical expansion of a multicomponent spin solution of the star-star relation with hyperbolic Boltzmann weights is investigated. The equations obtained in a quasi-class…
Algebraic entropy for hex systems
Giorgio Gubbiotti, Andrew P. Kels, Claude-M. Viallet
Hex systems were recently introduced [A. P. Kels. Integrable systems on hexagonal lattices and consistency on polytopes with quadrilateral and hexagonal faces. 2022. arXiv:2205.027…
Integrable systems on hexagonal lattices and consistency on polytopes with quadrilateral and hexagonal faces
Andrew P. Kels
The new concept of a system of hex equations is introduced as an overdetermined system of six five-point face-centered quad equations defined on six vertices of a hexagon. For a co…
Discrete integrable equations on face-centered cubics: consistency and Lax pairs of corner equations
Andrew P. Kels
A new set of discrete integrable equations, called face-centered quad equations, was recently obtained using new types of interaction-round-a-face solutions of the classical Yang-B…
Algebraic entropy for face-centered quad equations
Giorgio Gubbiotti, Andrew P. Kels
In this paper we define the algebraic entropy test for face-centered quad equations, which are equations defined on vertices of a quadrilateral plus an additional interior vertex.…
Entanglement of two disjoint intervals in conformal field theory and the 2D Coulomb gas on a lattice
Tamara Grava, Andrew P. Kels, Erik Tonni
In the conformal field theories given by the Ising and Dirac models, when the system is in the ground state, the moments of the reduced density matrix of two disjoint intervals and…
Lax matrices for lattice equations which satisfy consistency-around-a-face-centered-cube
Andrew P. Kels
There is a recently discovered formulation of the multidimensional consistency integrability condition for lattice equations, called consistency-around-a-face-centered-cube(CAFCC),…
Interaction-round-a-face and consistency-around-a-face-centered-cube
Andrew P. Kels
There is a correspondence between integrable lattice models of statistical mechanics and discrete integrable equations which satisfy multidimensional consistency, where the latter…
Two-component Yang-Baxter maps and star-triangle relations
Andrew P. Kels
It is shown how Yang-Baxter maps may be directly obtained from classical counterparts of the star-triangle relations and quantum Yang-Baxter equations. This is based on reinterpret…
Extended Z-invariance for integrable vector and face models and multi-component integrable quad equations
Andrew P. Kels
In a previous paper, the author has established an extension of the Z-invariance property for integrable edge-interaction models of statistical mechanics, that satisfy the star-tri…
Lens Generalisation of -functions for the Elliptic Discrete Painlevé Equation
Andrew P. Kels, Masahito Yamazaki
We propose a new bilinear Hirota equation for -functions associated with the root lattice, that provides a "lens" generalisation of the -functions for the elliptic disc…
Integrable quad equations derived from the quantum Yang-Baxter equation
Andrew P. Kels
This paper presents an explicit correspondence between two different types of integrable equations; the quantum Yang-Baxter equation in its star-triangle relation form, and the cla…
Lens elliptic gamma function solution of the Yang-Baxter equation at roots of unity
Andrew P. Kels, Masahito Yamazaki
We study the root of unity limit of the lens elliptic gamma function solution of the star-triangle relation, for an integrable model with continuous and discrete spin variables. Th…
Exactly solved models on planar graphs with vertices in
Andrew P. Kels
It is shown how exactly solved edge interaction models on the square lattice, may be extended onto more general planar graphs, with edges connecting a subset of next nearest neighb…
Elliptic hypergeometric sum/integral transformations and supersymmetric lens index
Andrew P. Kels, Masahito Yamazaki
We prove a pair of transformation formulas for multivariate elliptic hypergeometric sum/integrals associated to the and root systems, generalising the formulas previou…
The star-triangle relation, lens partition function, and hypergeometric sum/integrals
Ilmar Gahramanov, Andrew P. Kels
The aim of the present paper is to consider the hyperbolic limit of an elliptic hypergeometric sum/integral identity, and associated lattice model of statistical mechanics previous…
Quasi-classical expansion of the star-triangle relation and integrable systems on quad-graphs
Vladimir V. Bazhanov, Andrew P. Kels, Sergey M Sergeev
In this paper we give an overview of exactly solved edge-interaction models, where the spins are placed on sites of a planar lattice and interact through edges connecting the sites…
New solutions of the star-triangle relation with discrete and continuous spin variables
Andrew P. Kels
A new solution to the star-triangle relation is given, for an Ising type model that involves interacting spins, that contain integer and real valued components. Boltzmann weights o…
A new solution of the star-triangle relation
Andrew. P. Kels
We obtain a new solution to the star-triangle relation for an Ising-type model with two kinds of spin variables at each lattice site, taking continuous real values and arbitrary in…
Comment on star-star relations in statistical mechanics and elliptic gamma-function identities
Vladimir V. Bazhanov, Andrew P. Kels, Sergey M. Sergeev
We prove a recently conjectured star-star relation, which plays the role of an integrability condition for a class of 2D Ising-type models with multicomponent continuous spin varia…