Related papers: Finite-size effects in exponential random graphs a…
A wide variety of complex networks (social, biological, information etc.) exhibit local clustering with substantial variation in the clustering coefficient (the probability of neighbors being connected). Existing models of large graphs…
We study the Gierer-Meinhardt model of reaction-diffusion on a site-disordered square lattice. Let $p$ be the site occupation probability of the square lattice. For $p$ greater than a critical value $p_c$, the steady state consists of…
We investigate the diagonal entropy for ground states of the extended Kitaev chains with extensive pairing and hopping terms. The systems contain rich topological phases equivalently represented by topological invariant winding numbers and…
We discuss finite-size effects in one disordered ${\lambda}{\phi}^{4}$ model defined in a $d$-dimensional Euclidean space. We consider that the scalar field satisfies periodic boundary conditions in one dimension and it is coupled with a…
We introduce and study a class of particle hopping models consisting of a single box coupled to a pair of reservoirs. Despite being zero-dimensional, in the limit of large particle number and long observation time, the current and activity…
With a tight binding treatment we examine amorphous conductors with gas-like disorder, or no correlations among the site positions. We consider an exponentially decaying hopping integral with range $l$, and the Inverse Participation Ratio…
Asymptotically entropy of chaotic systems increases linearly and the sensitivity to initial conditions is exponential with time: these two behaviors are related. Such relationship is the analogous of and under specific conditions has been…
We present the first analytic study of finite-size effects on critical diffusion above and below T_c of three-dimensional Ising-like systems whose order parameter is coupled to a conserved density. We also calculate the finite-size…
We propose a general procedure for extracting the running coupling constants of the underlying field theory of a given classical statistical model on a two-dimensional lattice, combining tensor network renormalization (TNR) and the…
For $L \times L$ square lattices with $L \le 20$ the 2D Ising spin glass with +1 and -1 bonds is found to have a strong correlation between the energy and the entropy of its ground states. A fit to the data gives the result that each…
The finite-size effects in critical phenomena of a thin film system are studied from a mean field (MF) approach with $\phi^4$ model for second-order phase transition. The influence of boundary condition on the critical properties are…
We present a unifying, consistent, finite-size-scaling picture for percolation theory bringing it into the framework of a general, renormalization-group-based, scaling scheme for systems above their upper critical dimensions $d_c$.…
The $2$-star model is the simplest exponential random graph model that displays complex behavior, such as degeneracy and phase transition. Despite its importance, this model has been solved only in the regime of dense connectivity. In this…
We study entanglement via the subsystem purity relative to bipartitions of arbitrary excited states in (1+1)-dimensional conformal field theory, equivalent to the scaling limit of one dimensional quantum critical systems. We compute the…
We study the relative entropy of highly excited quantum states. First, we sample states from the Wishart ensemble and develop a large-N diagrammatic technique for the relative entropy. The solution is exactly expressed in terms of…
The density of states and the optical conductivity of the doped Hubbard model on a Bethe lattice with infinite connectivities have been studied using an analytic variant of the Lanczos continued fraction method. The spectral weight of the…
We study the role of finite size effects on a metallic critical behavior near a q = 0 critical point and compare the results with the recent extensive quantum Monte-Carlo (QMC) study [Y. Schattner et al, PRX 6, 0231028]. This study found…
The finite-size scaling theory for continuous phase transition plays an important role in determining critical point and critical exponents from the size-dependent behaviors of quantities in the thermodynamic limit. For percolation phase…
The exact numerical diagonalization and thermodynamics in an ensemble of small Hubbard clusters in the ground state and finite temperatures reveal intriguing insights into the nascent charge and spin pairings, Bose condensation and…
Ensemble models of graphs are one of the most important theoretical tools to study complex networks. Among them, exponential random graphs (ERGs) have proven to be very useful in the analysis of social networks. In this paper we develop a…