Related papers: Thermodynamic analysis of diverse percolation tran…
We investigate percolation, a probabilistic model for continuous phase transition (CPT), on square and weighted planar stochastic lattices. In its thermal counterpart, entropy is minimally low where order parameter (OP) is maximally high…
Interacting systems can be studied as the networks where nodes are system units and edges denote correlated interactions. Although percolation on network is a unified way to model the emergence and propagation of correlated behaviours, it…
We study explosive percolation (EP) on Erd\"{o}s-R\'{e}nyi network for product rule (PR) and sum rule (SR). Initially, it was claimed that EP describes discontinuous phase transition, now it is well-accepted as a probabilistic model for…
This work analyzes a percolation model on the diamond hierarchical lattice (DHL), where the percolation transition is retarded by the inclusion of a probability of erasing specific connected structures. It has been inspired by the recent…
We investigate the low-temperature critical behavior of the three dimensional random-field Ising ferromagnet. By a scaling analysis we find that in the limit of temperature $T \to 0$ the usual scaling relations have to be modified as far as…
We present the results of a percolation-like model that has been restricted compared to standard percolation models in the sense that we do not allow finite sized clusters to break up once they have formed. We calculate the critical…
In a new type of percolation phase transition, which was observed in a set of non-equilibrium models, each new connection between vertices is chosen from a number of possibilities by an Achlioptas-like algorithm. This causes preferential…
In phase transition phenomena, the estimation of the critical point is crucial for the calculation of the various critical exponents and the determination of the universality class they belong to. However, this is not an easy task, since a…
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 recent proliferation of correlated percolation models---models where the addition of edges/vertices is no longer independent of other edges/vertices---has been motivated by the quest to find discontinuous percolation transitions. The…
In two space dimensions, the percolation point of the pure-site clusters of the Ising model coincides with the critical point T_c of the thermal transition and the percolation exponents belong to a special universality class. By introducing…
The explosive percolation problem on the complete graph is investigated via extensive numerical simulations. We obtain the cluster-size distribution at the moment when the cluster size heterogeneity becomes maximum. The distribution is…
Recently, a hybrid percolation transitions (HPT) that exhibits both a discontinuous transition and critical behavior at the same transition point has been observed in diverse complex systems. In spite of considerable effort to develop the…
We study the structure and the dynamics in the formation of irreversible gels by means of molecular dynamics simulation of a model system where the gelation transition is due to the random percolation of permanent bonds between neighboring…
Although an intimate relation between entropy and diffusion has been advocated for many years and even seems to have been verified in theory and experiments, a quantitatively reliable study, and any derivation of an algebraic relation…
In systems undergoing second order phase transitions, the temperature integral of the specific heat over temperature from zero to the critical temperature is the same in both the normal and ordered phases. This entropy balance relates the…
Based on the foundations of thermodynamics and the equilibrium conditions for the coexistence of two phases in a magnetic Ising-like system, we show, first, that there is a critical point where the isothermal susceptibility diverges and the…
We conducted Monte Carlo simulations to analyze the percolation transition of a non-symmetric loop model on a regular three-dimensional lattice. We calculated the critical exponents for the percolation transition of this model. The…
Recent experiments and computer simulations show that supercooled liquids around the glass transition temperature are "dynamically heterogeneous" [1]. Such heterogeneity is expected from the random first order transition theory of the glass…
Disagreement percolation connects a Gibbs lattice gas and i.i.d. site percolation on the same lattice such that non-percolation implies uniqueness of the Gibbs measure. This work generalises disagreement percolation to the hard-sphere model…