Related papers: Critical behavior of $k$-core percolation: Numeric…

This work extends the thermodynamic analysis of random bond percolation to explosive and hybrid percolation models. We show that this thermodynamic analysis is well applicable to both explosive and hybrid percolation models by using the…

The study of the Ising model from a percolation perspective has played a significant role in the modern theory of critical phenomena. We consider the celebrated square-lattice Ising model and construct percolation clusters by placing bonds,…

We analytically describe the architecture of randomly damaged uncorrelated networks as a set of successively enclosed substructures -- k-cores. The k-core is the largest subgraph where vertices have at least k interconnections. We find the…

We consider a modification of the contact process incorporating higher-order reaction terms. The original contact process exhibits a non-equilibrium phase transition belonging to the universality class of directed percolation. The…

Recently, the number of non-standard percolation models has proliferated. In all these models, there exists a phase transition at which long range connectivity is established, if local connectedness increases through a threshold $p_c$. In…

We study multifractality in a broad class of disordered systems which includes, e.g., the diluted x-y model. Using renormalized field theory we analyze the scaling behavior of cumulant averaged dynamical variables (in case of the x-y model…

We consider the contact process near an extended surface defect, where the local control parameter deviates from the bulk one by an amount of $\lambda(l)-\lambda(\infty) = A l^{-s}$, $l$ being the distance from the surface. We concentrate…

We study FK-percolation where the edge parameters are chosen as independent random variables in the near-critical regime. We show that if these parameters satisfy a natural centering condition around the critical point, then the quenched…

We study the percolation transition of the geometrical clusters in the square lattice LCCC model (a kinetic opinion exchange model introduced by Lallouache et al. in Phys. Rev. E 82 056112 (2010)) with the change in conviction and…

Percolation is one of the most studied processes in statistical physics. A recent paper by Achlioptas et al. [Science 323, 1453 (2009)] has shown that the percolation transition, which is usually continuous, becomes discontinuous…

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…

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…

First-order phase transitions, classical or quantum, subject to randomness coupled to energy-like variables (bond randomness) can be rounded, resulting in continuous transitions (emergent criticality). We study perhaps the simplest such…

Hypergraphs are higher-order networks that capture the interactions between two or more nodes. Hypergraphs can always be represented by factor graphs, i.e. bipartite networks between nodes and factor nodes (representing groups of nodes).…

Binder liked ratios of baryon number are firstly suggested in relativistic heavy ion collisions. Using 3D-Ising model, the critical behavior of Binder ratios and ratios of high order cumulants of order parameter are fully presented. Binder…

The model of a one-dimensional kinetic contact process with parallel update is studied by the Monte Carlo simulations and finite-size scaling. The goal was to reveal the structure of the hidden percolative patterns (order parameters) in the…

Topological phase transitions can be described by the theory of critical phenomena and identified by critical exponents that define their universality classes. This is a consequence of the existence of a diverging length at the transition…

We report numerical evidence that an epidemic-like model, which can be interpreted as the propagation of a rumor, exhibits critical behavior at a finite randomness of the underlying small-world network. The transition occurs between a…

Many non-equilibrium systems display dynamic phase transitions from active to absorbing states, where fluctuations cease entirely. Based on a field theory representation of the master equation, the critical behavior can be analyzed by means…

We propose a numerical method to evaluate the upper critical dimension $d_c$ of random percolation clusters in Erd\H{o}s-R\'{e}nyi networks and in scale-free networks with degree distribution ${\cal P}(k) \sim k^{-\lambda}$, where $k$ is…