Related papers: Scaling limit for subsystems and Doplicher-Roberts…
We show that fractality in complex networks arises from the geometric self-similarity of their built-in hierarchical community-like structure, which is mathematically described by the scale-invariant equation for the masses of the boxes…
Scaling describes how a given quantity $Y$ that characterizes a system varies with its size $P$. For most complex systems it is of the form $Y\sim P^\beta$ with a nontrivial value of the exponent $\beta$, usually determined by regression…
Understanding the behaviour of topologically ordered lattice systems at finite temperature is a way of assessing their potential as fault-tolerant quantum memories. We compute the natural extension of the topological entanglement entropy…
Finite-size scaling, finite-size corrections, and boundary effects for critical systems have attracted much attention in recent years. Here we derive exact finite-size corrections for the free energy F and the specific heat C of the…
A scale-free network is grown in the Euclidean space with a global directional bias. On a vertical plane, nodes are introduced at unit rate at randomly selected points and a node is allowed to be connected only to the subset of nodes which…
We consider large uniform random trees where we fix for each vertex its degree and height. We prove, under natural conditions of convergence for the profile, that those trees properly renormalized converge. To this end, we study the paths…
Accepting validity of self-consistent theory of localization by Vollhardt and Woelfle, we derive the relations of finite-size scaling for different parameters characterizing the level statistics. The obtained results are compared with the…
The topology of the network of load transmitting connections plays an essential role in the cascading failure dynamics of complex systems driven by the redistribution of load after local breakdown events. In particular, as the network…
We classify Haag-dual Poincar\'e covariant subsystems $\B\subset \F$ of a graded-local net $\F$ on 4D Minkowski spacetime which satisfies standard assumptions and has trivial superselection structure. The result applies to the canonical…
Self-organized bistability (SOB) stands as a critical behavior for the systems delicately adjusting themselves to the brink of bistability, characterized by a first-order transition. Its essence lies in the inherent ability of the system to…
We consider scalar local operators of the determinant type in the conformal ``fishnet'' theory that arises as a limit of gamma-deformed $\mathcal{N}=4$ super Yang-Mills theory. We generalise a field-theory approach to expand their…
Spatial networks of land cover are well-described by power law rank-size distributions. Continuous field proxies for human settlements, agriculture and forest cover have similar spatial scaling properties spanning 4 to 5 orders of…
We propose a generic scaling theory for critical phenomena that includes power-law and essential singularities in finite and infinite dimensional systems. In addition, we clarify its validity by analyzing the Potts model in a simple…
We consider defect operators in scalar field theories in dimensions $d=4-\epsilon $ and $d=6-\epsilon$ with self-interactions given by a general marginal potential. In a double scaling limit, where the bulk couplings go to zero and the…
Independent random signs can govern various discrete models that converge to non-isomorphic continuous limits. Convergence of Fourier-Walsh spectra is established under appropriate conditions.
Subgraphs reveal information about the geometry and functionalities of complex networks. For scale-free networks with unbounded degree fluctuations, we obtain the asymptotics of the number of times a small connected graph occurs as a…
We derive conditions for the existence of fixed points of cone mappings without assuming scalability of functions. Monotonicity and scalability are often inseparable in the literature in the context of searching for fixed points of…
An intuitive overview of the scalability of a variety of types of wireless networks is presented. Simple heuris- tic arguments are demonstrated here for scaling laws presented in other works, as well as for conditions not previously…
Consider a Hausdorff space (X,T) and a set C of converging nets in X. By virtue of the limit uniqueness, the relation Lim which assigns each member x of X to every net N lying in C that converges to x is a map. Of course, structuring C with…
We study conformal boundary conditions for the theory of a single real scalar to investigate whether the known Dirichlet and Neumann conditions are the only possibilities. For this free bulk theory there are strong restrictions on the…