Related papers: The anisotropic Ising correlations as elliptic int…
We show that the globally nilpotent G-operators corresponding to the factors of the linear differential operators annihilating the multifold integrals $\chi^{(n)}$ of the magnetic susceptibility of the Ising model ($n \le 6$) are…
We show that the n-fold integrals $\chi^{(n)}$ of the magnetic susceptibility of the Ising model, as well as various other n-fold integrals of the "Ising class", or n-fold integrals from enumerative combinatorics, like lattice Green…
Elliptic functions are largely studied and standardized mathematical objects. The two usual approaches are due to Jacobi and Weierstrass. From a contour integral which allowed us to unify many summation formulae (Euler-MacLaurin, Poisson,…
We explore short-distance static correlation functions in the infinite XXZ chain using previously derived formulae which represent the correlation functions in factorized form. We compute two-point functions ranging over 2, 3 and 4 lattice…
Defects associated with non-invertible symmetries have attracted significant attention in recent years. Among them, Kramers-Wannier (KW) duality defects have been investigated in both classical statistical systems and quantum Hamiltonian…
In this paper, we study polar harmonic Maass forms of negative integral weight. Using work of Fay, we construct Poincar\'e series which span the space of such forms and show that their elliptic coefficients exhibit duality properties which…
In a recent paper [P. Mayer et al., Phys. Rev. Lett. 93, 115701 (2004)] it was shown, by means of experiments, theory and simulations, that coarsening systems display dynamic heterogeneity analogous to that of glass formers. Here, we…
In this work we propose a novel approach to integrate the Lane-Emden equations for relativistic anisotropic polytropes. We take advantage of the fact that Gravitational Decoupling allows to decrease the number of degrees of freedom once a…
The classical concept of $Q$-functions associated to symmetric and selfadjoint operators due to M.G. Krein and H. Langer is extended in such a way that the Dirichlet-to-Neumann map in the theory of elliptic differential equations can be…
We prove explicit doubling inequalities and obtain uniform upper bounds (under $(d-1)$-dimensional Hausdorff measure) of nodal sets of weak solutions for a family of linear elliptic equations with rapidly oscillating periodic coefficients.…
In this paper we show, in a systematic way, how to relate the Kepler problem to the isotropic harmonic oscillator. Unlike previous approaches, our constructions are carried over in the Lagrangian formalism dealing with second order vector…
The all-loop anisotropic Thirring model interpolates between the WZW model and the non-Abelian T-dual of the anisotropic principal chiral model. We focus on the SU(2) case and we prove that it is classically integrable by providing its Lax…
Interpretation of dispersionless integrable hierarchies as equations of coisotropic deformations for certain algebras and other algebraic structures like Jordan triple systInterpretation of dispersionless integrable hierarchies as equations…
A fully anisotropic simple-cubic Ising lattice in the geometry of periodic cylinders $n\times n\times\infty$ is investigated by the transfer-matrix finite-size scaling method. In addition to the previously obtained critical amplitudes of…
We consider families of multiple and simple integrals of the ``Ising class'' and the linear ordinary differential equations with polynomial coefficients they are solutions of. We compare the full set of singularities given by the roots of…
For a family of second-order elliptic operators with rapidly oscillating periodic coefficients, we study the asymptotic behavior of the Green and Neumann functions, using Dirichlet and Neumann correctors. As a result we obtain asymptotic…
A superintegrable, discrete model of the quantum isotropic oscillator in two-dimensions is introduced. The system is defined on the regular, infinite-dimensional $\mathbb{N}\times \mathbb{N}$ lattice. It is governed by a Hamiltonian…
In this paper, we propose a numerical method to solve isotropic elliptic equations on point cloud by generalizing the point integral method. The idea of the point integral method is to approximate the differential operators by integral…
We investigate a two-dimensional Ising model with long-range interactions that emerge from a generalization of the magnetic dipolar interaction in spin systems with in-plane spin orientation. This interaction is, in general, anisotropic…
We examine the reductions of the order of certain third- and second-order nonlinear equations with arbitrary nonlinearity through their symmetries and some appropriate transformations. We use the folding transformation which enables one to…