Related papers: The non-linear supersymmetric hyperbolic sigma mod…
Discrete fermionic and bosonic models for hyperbolic lattices have attracted significant attention across a range of fields since the experimental realization of hyperbolic lattices in metamaterial platforms, sparking the development of…
We use properties of symplectic capacities that were recently defined by Hutchings to obtain upper bounds on the minimal action of Reeb orbits on fiberwise star-shaped hypersurfaces $\Sigma \subset T^*S^2$. In addition, we introduce the…
This paper is devoted to discuss the stabilizability of a class of $ 2 \times2 $ non-homogeneous hyperbolic systems. Motivated by the example in \cite[Page 197]{CB2016}, we analyze the influence of the interval length $L$ on stabilizability…
This paper is a letter-type version of hep-th/9806236. We discuss properties of non-linear equations of motion which describe higher-spin gauge interactions for massive spin-0 and spin-1/2 matter fields in 2+1 dimensional anti-de Sitter…
We study statistical and algorithmic aspects of using hypergraphons, that are limits of large hypergraphs, for modeling higher-order interactions. Although hypergraphons are extremely powerful from a modeling perspective, we consider a…
We show how a Heisenberg spin chain emerges from the two-dimensional ${\mathcal N}$=(2,2) gauge theory at an intermediate scale, which relies on the renormalization group flow guided by the global symmetries and the dynamics of domain…
We study random covers of a closed hyperbolic surface $\Sigma$, subject to the condition that, for $k\geq 2$, the fundamental group is isomorphic to the free group $F_k$. We show that asymptotically they distribute according to a specific…
In this paper we consider the existence of Hamilton cycles and perfect matchings in a random graph model proposed by Krioukov et al.~in 2010. In this model, nodes are chosen randomly inside a disk in the hyperbolic plane and two nodes are…
We study the spin-$1/2$ Ising chain with multispin interactions $K$ involving the product of $m$ successive spins, for general values of $m$. Using a change of spin variables the zero-field partition function of a finite chain is obtained…
Recently, Schmidt et al. proved that the energy spectrum of a Heisenberg spin system (HSS) is bounded by two parabolas, i.e. lines which depend on the total spin quantum number S as S(S+1). The prove holds for homonuclear HSSs which fulfill…
We discuss three questions related to the critical behavior of hierarchical spin models: 1) the hyperscaling relations in the broken symmetry phase; 2) the combined use of dual expansions to calculate the non-universal quantities; 3) the…
Supersymmetric nonlinear sigma models have target spaces that carry interesting geometry. The geometry is richer the more supersymmetries the model has. The study of models with two dimensional world sheets is particularly rewarding since…
Methods for understanding classical disordered spin systems with interactions conforming to some idealized graphical structure are well developed. The equilibrium properties of the Sherrington-Kirkpatrick model, which has a densely…
The intricate relations between elements in natural and human-made systems sustain the complex processes that shape our world, forming multiscale networks of interactions. These networks can be represented as graphs composed of nodes…
We investigate analogues of some of the classical results in homogeneous dynamics in non-linear setting. Let $G$ be a closed subgroup of the group of automorphisms of a biregular tree and $\Gamma<G$ a discrete subgroup. For a large class of…
We report our density matrix renormalization-group and analytical work on S=1 antiferromagnetic Heisenberg spin chains. We study the finite size behavior within the framework of the non-linear sigma model. We study the effect of…
The basic interaction unit of many dynamical systems involves more than two nodes. In such situations where networks are not an appropriate modelling framework, it has recently become increasingly popular to turn to higher-order models,…
We analyse the global symmetry structure of two-dimensional Non-Linear Sigma Models with Wess-Zumino term. When the target space has a compact isometry without fixed points, the theory has a pair of (group-like) global symmetries and many…
Compact (ferro- and antiferromagnetic) sigma-models and noncompact (hyperbolic) sigma-models are compared in a lattice formulation in dimensions $d \geq 2$. While the ferro- and antiferromagnetic models are essentially equivalent, the…
We describe a N=2 supersymmetric extension of the nonrelativistic (2+1)-dimensional model describing particles on the noncommutative plane with scalar (electric) and vector (magnetic) interactions. First, we employ the N=2 superfield…