相关论文: Critical behavior of two-choice rules: a class of …
The class of random-cluster models is a unification of a variety of stochastic processes of significance for probability and statistical physics, including percolation, Ising, and Potts models; in addition, their study has impact on the…
We study the class of monotone, two-state, deterministic cellular automata, in which sites are activated (or 'infected') by certain configurations of nearby infected sites. These models have close connections to statistical physics, and…
Preferential attachment networks with power law exponent $\tau>3$ are known to exhibit a phase transition. There is a value $\rho_{\rm c}>0$ such that, for small edge densities $\rho\leq \rho_c$ every component of the graph comprises an…
In extensive Monte Carlo simulations the phase transition of the random field Ising model in three dimensions is investigated. The values of the critical exponents are determined via finite size scaling. For a Gaussian distribution of the…
The critical phase of bond percolation on the random growing tree is examined. It is shown that the root cluster grows with the system size $N$ as $N^\psi$ and the mean number of clusters with size $s$ per node follows a power function $n_s…
We propose a self-adapted Monte Carlo approach to automatically determine the critical temperature by simulating two systems with different sizes at the same temperature. The temperature is increased or decreased by checking the short-time…
We propose a simple random process inducing various types of random graphs and the scale free random graphs among others. The model is of a threshold nature and differs from the preferential attachment approach discussed in the literature…
In this paper we determine a class of critical sets in the abelian {2--group} that may be obtained from a greedy algorithm. These new critical sets are all 2--critical (each entry intersects an intercalate, a trade of size 4) and completes…
Dynamical processes on complex networks, ranging from biological, technological and social systems, show phase transitions between distinct global states of the system. Often, such transitions rely upon the interplay between the structure…
We analyze critical phenomena on networks generated as the union of hidden variables models (networks with any desired degree sequence) with arbitrary graphs. The resulting networks are general small-worlds similar to those a` la Watts and…
We provide sufficient conditions for a regular graph $G$ of growing degree $d$, guaranteeing a phase transition in its random subgraph $G_p$ similar to that of $G(n,p)$ when $p\cdot d\approx 1$. These conditions capture several well-studied…
We study the critical behavior of the component sizes for the configuration model when the tail of the degree distribution of a randomly chosen vertex is a regularly-varying function with exponent $\tau-1$, where $\tau\in (3,4)$. The…
We consider self-loops and multiple edges in the configuration model as the size of the graph tends to infinity. The interest in these random variables is due to the fact that the configuration model, conditioned on being simple, is a…
Critical behaviour of a fluid, subjected to strongly anisotropic turbulent mixing, is studied by means of the field theoretic renormalization group. As a simplified model, relaxational stochastic dynamics of a non-conserved scalar order…
Critical exponents have been obtained for a 3D spin particle system. Clusters are formed and system reaches a critical behavior when fragment size distribution follows a power law, as predicted by Fisher Liquid Droplet Model. Also,…
Two dimensional condensed matter is realised in increasingly diverse forms that are accessible to experiment and of potential technological value. The properties of these systems are influenced by many length scales and reflect both generic…
We offer a solution to a long-standing problem in the physics of networks, the creation of a plausible, solvable model of a network that displays clustering or transitivity -- the propensity for two neighbors of a network node also to be…
Many real-world networks exhibit the so-called small-world phenomenon: their typical distances are much smaller than their sizes. One mathematical model for this phenomenon is a long-range percolation graph on a $d$-dimensional box $\{0, 1,…
We propose an iterative proposal to estimate critical points for statistical models based on configurations by combing machine-learning tools. Firstly, phase scenarios and preliminary boundaries of phases are obtained by…
This paper studies the critical and near-critical regimes of the planar random-cluster model on $\mathbb Z^2$ with cluster-weight $q\in[1,4]$ using novel coupling techniques. More precisely, we derive the scaling relations between the…