相关论文: Universality Diagram of Phase Transitions in Long-…
Percolation is the simplest fundamental model in statistical mechanics that exhibits phase transitions signaled by the emergence of a giant connected component. Despite its very simple rules, percolation theory has successfully been applied…
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…
It is well established that the phase transition between survival and extinction in spreading models with short-range interactions is generically associated with the directed percolation (DP) universality class. In many realistic spreading…
Universal scaling laws only apply asymptotically near critical phase transitions. We propose a general scheme, based on normal form theory of renormalization group flows, for incorporating corrections to scaling that quantitatively describe…
The percolation study offers valuable insights into the characteristics of phase transition, shedding light on the underlying mechanisms that govern the formation of global connectivity within the system. We explore the percolation phase…
We consider a class of percolation models where the local occupation variables have long-range correlations decaying as a power law $\sim r^{-a}$ at large distances $r$, for some $0< a< d$ where $d$ is the underlying spatial dimension. For…
A relatively simple and physically transparent model based on quantum percolation and dephasing is employed to construct a global phase diagram which encodes and unifies the critical physics of the quantum Hall, "two-dimensional…
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…
Determining the threshold value $\sigma_*$ that separates the short-range (SR) and long-range (LR) universality classes in phase transitions remains a controversial issue. While Sak's criterion, $\sigma_* = 2 - \eta_{\mathrm{SR}}$, has been…
A coarse-grained description of the restricted primitive model is considered in terms of the local charge- and number-density fields. Exact reduction to a one-field theory is derived, and exact expressions for the number-density correlation…
Cluster percolation and second order thermal phase transitions show an amazing number of common features: power laws of the variables at criticality, scaling relations of the critical exponents and universality of the critical indices.…
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…
Our community has a deep and sophisticated understanding of phase transitions and their universal scaling functions. We outline and advocate an ambitious program to use this understanding as an anchor for describing the surrounding phases.…
By performing a high-statistics simulation of the $D=4$ random-field Ising model at zero temperature for different shapes of the random-field distribution, we show that the model is ruled by a single universality class. We compute to a high…
We study nonequilibrium phase transitions of reaction-diffusion systems defined on randomly diluted lattices, focusing on the transition across the lattice percolation threshold. To develop a theory for this transition, we combine classical…
We perform large-scale simulations of the two-dimensional long-range bond percolation model with algebraically decaying percolation probabilities $\sim 1/r^{2+\sigma}$, using both conventional ensemble and event-based ensemble methods for…
We analyse the critical properties of a weakly diluted (random) Ising model with the long-range interaction decaying with distance $x$ as $\sim x^{-d-\sigma}$ in a $d$-dimensional space. It is known to belong to a new long-range random…
The two-dimensional (zero magnetic field) Ising model is known to undergo a second order para-ferromagnetic phase transition, which is accompanied by a correlated percolation transition for the Fortuin-Kasteleyn (FK) clusters. In this paper…
Hierarchical lattices that constitute spatially anisotropic systems are introduced. These lattices provide exact solutions for hierarchical models and, simultaneously, approximate solutions for uniaxially or fully anisotropic d=3 physical…
The Voronoi construction is ubiquitous across the natural sciences and engineering. In statistical mechanics, though, critical phenomena have so far been only investigated on the Delaunay triangulation, the dual of a Voronoi graph. In this…