相关论文: Mesoscopic scales in hierarchical configuration mo…
We study the connected components in critical percolation on the Hamming hypercube $\{0,1\}^m$. We show that their sizes rescaled by $2^{-2m/3}$ converge in distribution, and that, considered as metric measure spaces with the graph distance…
We present simulation results for the contact process on regular, cubic networks that are composed of a one-dimensional lattice and a set of long edges with unbounded length. Networks with different sets of long edges are considered, that…
We consider the critical behavior of two-dimensional layered Ising models where the exchange couplings between neighboring layers follow hierarchical sequences. The perturbation caused by the non-periodicity could be irrelevant, relevant or…
We study the random connection model on hyperbolic space $\mathbb{H}^d$ in dimension $d=2,3$. Vertices of the spatial random graph are given as a Poisson point process with intensity $\lambda>0$. Upon variation of $\lambda$ there is a…
Recently, the concept of geometric renormalization group provides a good approach for studying the structural symmetry and functional invariance of complex networks. Along this line, we systematically investigate the finite-size scaling of…
One of the most remarkable social phenomena is the formation of communities in social networks corresponding to families, friendship circles, work teams, etc. Since people usually belong to several different communities at the same time,…
Kernel spectral clustering corresponds to a weighted kernel principal component analysis problem in a constrained optimization framework. The primal formulation leads to an eigen-decomposition of a centered Laplacian matrix at the dual…
We report on extensive numerical simulations of the three-dimensional Heisenberg model and its analysis through finite-size scaling of Lee-Yang zeros. Besides the critical regime, we also investigate scaling in the ferromagnetic phase. We…
Understanding how internal community structure shapes the course of epidemics remains a fundamental challenge in modeling real-world populations. Standard metapopulation models often assume uniform mixing within communities, overlooking how…
Berry phases and the quantum-information theoretic notion of fidelity have been recently used to analyze quantum phase transitions from a geometrical perspective. In this paper we unify these two approaches showing that the underlying…
Extensive studies have been done to understand the principles behind architectures of real networks. Recently, evidences for hierarchical organization in many real networks have also been reported. Here, we present a new hierarchical model…
We present simulations of stochastic fluid dynamics in the vicinity of a critical endpoint belonging to the universality class of the Ising model. This study is motivated by the challenge of modeling the dynamics of critical fluctuations…
A classification of critical behavior is provided in systems for which the renormalization group equations are control-parameter dependent. It describes phase transitions in networks with a recursive, hierarchical structure but appears to…
We apply a variant of the explosive percolation procedure to large real-world networks, and show with finite-size scaling that the university class, ordinary or explosive, of the resulting percolation transition depends on the structural…
The mean-field optical phase transition in multimode equal-coupling photonic networks is studied by temporal evolution of the nonlinear equations of motion of the coupled modes. Analogies to statistical mechanics models of interacting…
We consider a model for random hypergraphs with identifiability, an analogue of connectedness. This model has a phase transition in the proportion of identifiable vertices when the underlying random graph becomes critical. The phase…
We study the phase diagram of a class of models in which a generalized cluster interaction can be quenched by Ising exchange interaction and external magnetic field. We characterize the various phases through winding numbers. They may be…
In this paper we study the small-world network model of Watts and Strogatz, which mimics some aspects of the structure of networks of social interactions. We argue that there is one non-trivial length-scale in the model, analogous to the…
It is proposed that the $O(n)$ spin and geometrical percolation models can help to study the QCD phase diagram due to the universality properties of the phase transition. In this paper, correlations and fluctuations of various sizes of…
The talk presented at ICMP 97 focused on the scaling limits of critical percolation models, and some other systems whose salient features can be described by collections of random lines. In the scaling limit we keep track of features seen…