Related papers: Van der Waerden's Colouring Theorem and Classical …
The lambda model is a one parameter deformation of the principal chiral model that arises when regularizing the non-compactness of a non-abelian T dual in string theory. It is a current-current deformation of a WZW model that is known to be…
In the spirit of multi-scale modeling, we develop a theoretical framework for spin-lattice coupling that connects, on the one hand, to ab initio calculations of spin-lattice coupling parameters and, on the other hand, to the magneto-elastic…
The possibility of generating a color superconducting state in 2+1 dimensional QCD is analyzed. The gap equation in the leading, hard-dense loop improved, one-gluon exchange approximation is derived and solved. The magnitude of the order…
We conclude an investigation of Abrishami, Esperet, Giocanti, Hamman, Knappe and M\"oller studying the existence of periodic colourings of locally finite graphs. A colouring of a graph $\Gamma$ is periodic if the resulting coloured graph…
Working with anticommuting Weyl(or Mayorana) spinors in the framework of the van der Waerden calculus is standard in supersymmetry. The natural frame for rigorous supersymmetric quantum field theory makes use of operator-valued…
Van der Waerden's theorem asserts that if you color the natural numbers with, say, five different colors, then you can always find arbitrarily long sequences of numbers that have the same color and that form an arithmetic progression.…
Given the integral lattice $\Lambda^d$ in $d$-dimensional Euclidean space, partitions of the lattice nodes into orbits of finite-index subgroups of $Aut(\Lambda^d)$ have been computed for $d \leq 4$. These partitions can be interpreted as…
We present a phenomenological theory for coupled spin-charge dynamics in magnetic van der Waals heterostructures. The system studied consists of a layered antiferromagnet inserted into a capacitive vdW heterostructure. It has been recently…
We give Henneberg-type constructions for three families of sparse colored graphs arising in the rigidity theory of periodic and other forced symmetric frameworks. The proof method, which works with Laman-sparse finite covers of colored…
In this paper we have investigated some old issues concerning four color map problem. We have given a general method for constructing counter-examples to Kempe's proof of the four color theorem and then show that all counterexamples can be…
We consider a two-dimensional spin system in a honeycomb lattice configuration that exhibits anyonic and fermionic excitations [Kitaev, cond-mat/0506438]. The exact spectrum that corresponds to the translationally invariant case of a…
We study the 2D Ising model on a square lattice with additional non-equal diagonal next-nearest neighbor interactions. The cases of classical and quantum (transverse) models are considered. Possible phases and their locations in the space…
Bosonic colored group field theory is considered. Focusing first on dimension four, namely the colored Ooguri group field model, the main properties of Feynman graphs are studied. This leads to a theorem on optimal perturbative bounds of…
We built a model where all spins are in interaction with each other via an antiferromagnetic Ising Hamiltonian. The geometry of such a model is a tetrahedron placed on a hypersphere in spaces of dimensions enclosed between 1 and 9. Due to…
We develop a topological framework in an attempt to generalize the classical colourful Caratheodory theorem by imposing an additional constraint. For that we introduce the notion of zero-avoding complexes and covering criteria for the…
We study spinless bosons in a decorated square lattice with a near-diagonal tilt. The resonant subspace of the tilted Mott insulator is described by an effective Hamiltonian of frustrated quantum Ising spins on a non-bipartite lattice. This…
A vertex colouring of a graph $G$ is "nonrepetitive" if $G$ contains no path for which the first half of the path is assigned the same sequence of colours as the second half. Thue's famous theorem says that every path is nonrepetitively…
Within Euclidean lattice field theory an exact equivalence between the one-flavour 2D Thirring model with Wilson fermions and Wilson parameter $r = 1$ to a two-colour loop model on the square lattice is established. For non-interacting…
Given a set equipped with a transitive action of a group, we define the notion of an almost invariant coloring of the set. We consider the mapping class group orbit of a multicurve on a compact surface, and prove that in the case of genus…
Van der Waals "sliding" ferroelectric bilayers, whose electric polarization is locked to the interlayer alignment, show promise for future non-volatile memory and other nanoelectronic devices. These applications require a fuller…