Related papers: Cluster integrable systems and spin chains
We introduce a Poisson variety compatible with a cluster algebra structure and a compatible toric action on this variety. We study Poisson and topological properties of the union of generic orbits of this toric action. In particular, we…
In the framework of the semiclassical approach the universal spectral correlations in the Hamiltonian systems with classical chaotic dynamics can be attributed to the systematic correlations between actions of periodic orbits which (up to…
We formulate a new geometrical string on the euclidean lattice. It is possible to find such spin systems with local interaction which reproduce the same surface dynamics.In the three-dimensional case this spin system is a usual Ising…
We investigate the emergence of chimera and cluster states possessing asymmetric dynamics in globally coupled systems, where the trajectories of oscillators belonging to different subpopulations exhibit different dynamical properties. In an…
We use rich clusters of galaxies in the Northern and Southern Galactic hemispheres up to a redshift z=0.12 to determine the cluster correlation function. We show that superclusters of galaxies and voids between them form a moderately…
We review and compare the integrable structures in N=4 gauge theory and string theory on AdS5xS5. Recently, Bethe ansaetze for gauge theory/weak coupling and string theory/strong coupling were proposed to describe scaling dimensions in the…
We develop a theory to investigate how geometrically frustrated clusters that become decorated affect the Cluster Spin Glass phase. The cluster structure is assumed to be a tetrahedron composed of Ising spins with z-anisotropy placed at its…
Recent studies have shown that two widely-used mechanisms for single-transverse-spin asymmetries based on either twist-three contributions or on transverse-momentum-dependent (Sivers) parton distributions become identical in a kinematical…
We show the existence of quasi-cluster $\mathcal{A}$-structures and cluster Poisson structures on moduli stacks of sheaves with singular support in the alternating strand diagram of grid plabic graphs by studying the microlocal parallel…
Symmetries in a network connectivity regulate how the graph's functioning organizes into clustered states. Classical methods for tracing the symmetry group of a network require very high computational costs, and therefore they are of hard,…
The antiferromagnetic Heisenberg chain is expected to have an extended symmetry, [SU(2)xSU(2)]/Z 2 , in the infrared limit, whose physical interpretation is that the spin and dimer order parameters form the components of a common…
We consider a class of map, recently derived in the context of cluster mutation. In this paper we start with a brief review of the quiver context, but then move onto a discussion of a related Poisson bracket, along with the Poisson algebra…
We derive a general framework for describing semi-inclusive deep-inelastic lepton-nucleon scattering in terms of the unintegrated parton distributions and other higher twist parton correlations. Such a framework provides a consistent…
The two-point correlation function of chaotic systems with spin 1/2 is evaluated using periodic orbits. The spectral form factor for all times thus becomes accessible. Equivalence with the predictions of random matrix theory for the…
We initiate the study of cluster algebras in Feynman integrals in dimensional regularization. We provide evidence that four-point Feynman integrals with one off-shell leg are described by a $C_{2}$ cluster algebra, and we find cluster…
Using results on topological line defects of 4D Chern-Simons theory and the algebra/cycle homology correspondence in complex surfaces $\mathcal{S}$ with ADE singularities, we study the graded properties of the $sl(m|n)$ chain and its…
In this review we show that the multi-particle scattering amplitudes in N=4 SYM at large Nc and in the multi-Regge kinematics for some physical regions have the high energy behavior appearing from the contribution of the Mandelstam cuts in…
Massive higher spin fields are notoriously difficult to introduce interactions when they are described by symmetric (spin)-tensors. An alternative approach is to use chiral description that does not have unphysical longitudinal modes. For…
For a finite-dimensional simple Lie algebra $\mathfrak{g}$ admitting a non-trivial minuscule representation and a connected marked surface $\Sigma$ with at least two marked points and no punctures, we prove that the cluster algebra…
Dynamical systems on networks with adaptive couplings appear naturally in real-world systems such as power grid networks, social networks as well as neuronal networks. We investigate a paradigmatic system of adaptively coupled phase…