Related papers: Universality of percolation at dynamic pseudocriti…
The properties of the pure-site clusters of spin models, i.e. the clusters which are obtained by joining nearest-neighbour spins of the same sign, are here investigated. In the Ising model in two dimensions it is known that such clusters…
We present a new unified theory of critical finite-size scaling for lattice statistical mechanical models with periodic boundary conditions above the upper critical dimension. Our theory is based on recent mathematically rigorous results…
We consider a type of dependent percolation introduced by Aizenman and Grimmett, who showed that certain "enhancements" of independent (Bernoulli) percolation, called essential, make the percolation critical probability strictly smaller. In…
It is a central prediction of renormalisation group theory that the critical behaviours of many statistical mechanics models on Euclidean lattices depend only on the dimension and not on the specific choice of lattice. We investigate the…
Jamming and percolation transitions in the standard random sequential adsorption of particles on regular lattices are characterized by a universal set of critical exponents. The universality class is preserved even in the presence of…
The distribution of masses of clusters smaller than the infinite cluster is evaluated at the percolation threshold. The clusters are ranked according to their masses and the distribution $P(M/L^D,r)$ of the scaled masses M for any rank r…
The theory of continuous phase transitions predicts the universal collective properties of a physical system near a critical point, which for instance manifest in characteristic power-law behaviours of physical observables. The…
How does the percolation transition behave in the absence of quenched randomness? To address this question, we study two nonrandom self-dual quasiperiodic models of square-lattice bond percolation. In both models, the critical point has…
Universality is a fundamental concept in modern physics. For the $q$-state Potts model, the critical exponents are merely determined by the order-parameter symmetry $S_q$, spatial dimensionality and interaction range, independent of…
One of the most impressive features of continuous phase transitions is the concept of universality, that allows to group the great variety of different critical phenomena into a small number of universality classes. All systems belonging to…
In this work we analyze the universal scaling functions and the critical exponents at the upper critical dimension of a continuous phase transition. The consideration of the universal scaling behavior yields a decisive check of the value of…
We study a class of one-matrix models with an action containing nonpolynomial terms. By tuning the coupling constants in the action to criticality we obtain that the eigenvalue density vanishes as an arbitrary real power at the origin, thus…
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 describe the critical window for percolation in the universality class of sparse growing random graphs. In our models, vertices arrive sequentially and connect independently to each earlier vertex $v$ with probability proportional to a…
Critical points and singularities are encountered in the study of critical phenomena in probability and physics. We present recent results concerning the values of such critical points and the nature of the singularities for two prominent…
We report on universality in boundary domain growth in cluster aggregation in the limit of maximum concentration. Maximal concentration means that the diffusivity of the clusters is effectively zero and, instead, clusters merge successively…
Universal behavior is a typical emergent feature of critical systems. A paramount model of the non-equilibrium critical behavior is the directed bond percolation process that exhibits an active- to-absorbing state phase transition in the…
Regardless of model and platform details, the critical phenomena exhibit universal behaviors that are remarkably consistent across various experiments and theories, resulting in a significant scientific success of condensed matter physics.…
A wide variety of methods have been used to compute percolation thresholds. In lattice percolation, the most powerful of these methods consists of microcanonical simulations using the union-find algorithm to efficiently determine the…
The development of percolation theory was historically shaped by its numerous applications in various branches of science, in particular in statistical physics, and was mainly constrained to the case of Euclidean spaces. One of its central…