Related papers: Scaling limit for subsystems and Doplicher-Roberts…
We present the finite-size scaling theory of one-dimensional quantum critical systems in the presence of boundaries. While the finite-size spectrum in the conformal limit, namely of a conformal field theory with conformally invariant…
Connectivity correlations play an important role in the structure of scale-free networks. While several empirical studies exist, there is no general theoretical analysis that can explain the largely varying behavior of real networks. Here,…
The paper studies scaling limits of random skew plane partitions confined to a box when the inner shapes converge uniformly to a piecewise linear function V of arbitrary slopes in [-1,1]. It is shown that the correlation kernels in the bulk…
We study the effects of a power-law trapping potential on the scaling behaviour of the entanglement at the quantum critical point of one-dimensional (1D) lattice particle systems. We compute bipartite von Neumann and Renyi entropies in the…
We report on parallel observations in two seemingly unrelated areas of dynamical network research. The one is the so-called small world phenomenon and/or the observation of scale freeness in certain types of large (empirical) networks and…
We investigate the fundamental principles that drive the development of scalable algorithms for network optimization. Despite the significant amount of work on parallel and decentralized algorithms in the optimization community, the methods…
In this article we give new examples of models in boundary quantum field theory, i.e. local time-translation covariant nets of von Neumann algebras, using a recent construction of Longo and Witten, which uses a local conformal net A on the…
We discuss how various models of scale-free complex networks approach their limiting properties when the size N of the network grows. We focus mainly on equilibrated networks and their finite-size degree distributions. Our results show that…
For any given algebra of local observables in Minkowski space an associated scaling algebra is constructed on which renormalization group (scaling) transformations act in a canonical manner. The method can be carried over to arbitrary…
The finite-size scaling function and the leading corrections for the single species 1D coagulation model $(A + A \rightarrow A)$ and the annihilation model $(A + A \rightarrow \emptyset)$ are calculated. The scaling functions are universal…
In an arbitrary unitary 4D CFT we consider a scalar operator \phi, and the operator \phi^2 defined as the lowest dimension scalar which appears in the OPE \phi\times\phi with a nonzero coefficient. Using general considerations of OPE,…
A finite-size-scaling (FSS) theory is proposed for various models in complex networks. In particular, we focus on the FSS exponent, which plays a crucial role in analyzing numerical data for finite-size systems. Based on the…
We study the statistical properties of observables of scale-free networks in the degree-thresholding renormalization (DTR) flows. For BA scale-free networks with different sizes, we find that their structural and dynamical observables have…
The presence of large-scale real-world networks with various architectures has motivated an active research towards a unified understanding of diverse topologies of networks. Such studies have revealed that many networks with the scale-free…
Fixed points of scalar field theories with quartic interactions in $d=4-\varepsilon$ dimensions are considered in full generality. For such theories it is known that there exists a scalar function $A$ of the couplings through which the…
We analyze the degree distribution's cut-off in finite size scale-free networks. We show that the cut-off behavior with the number of vertices $N$ is ruled by the topological constraints induced by the connectivity structure of the network.…
Small-world networks, known for high local clustering and short path lengths, are a fundamental structure in many real-world systems, including social, biological, and technological networks. We apply the theory of (marked) local…
We investigate critical $N$-component scalar field theories and the spontaneous breaking of scale invariance in three dimensions using functional renormalisation. Global and local renormalisation group flows are solved analytically in the…
In this paper, we use crossing symmetry and unitarity constraints to put a lower bound on the central charge of conformal field theories in large space-time dimensions $D$. Specifically, we work with the four-point function of identical…
The scaling of entanglement entropy is computationally studied in several $1\le d \le 2$ dimensional free fermion systems that are connected by one or more point contacts (PC). For both the $k$-leg Bethe lattice $(d =1)$ and $d=2$…