Related papers: The Percolation Transition in the Zero-Temperature…
We investigate the geometry of a typical spin cluster in random triangulations sampled with a probability proportional to the energy of an Ising configuration on their vertices, both in the finite and infinite volume settings. This model is…
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…
At low temperatures, the classical two-dimensional random bond Ising model undergoes a frustration-driven ferromagnet-to-paramagnet transition controlled by a zero-temperature fixed point separating ferromagnet and spin glass phases. We…
One-dimensional non-equilibrium kinetic Ising models evolving under the competing effect of spin flips at zero temperature and nearest-neighbour spin exchanges exhibiting directed percolation-like parity conserving(PC) phase transition on…
We present extensive molecular dynamics simulations of a liquid of symmetric dumbbells, for constant packing fraction, as a function of temperature and molecular elongation. For large elongations, translational and rotational degrees of…
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…
Statistical spin dynamics plays a key role to understand the working principle for novel optical Ising machines. Here we propose the gauge transformations for spatial photonic Ising machine, where a single spatial phase modulator…
In the paper the Pair Approximation (PA) method for studies of the site-diluted spin-1/2 systems of arbitrary dimensionality with the long-range ferromagnetic interactions is adopted. The method allows to take into account arbitrary…
In this paper, the phase diagrams and the critical behavior of the spin-1/2 anisotropic XXZ ferromagnetic model (the anisotropic parameter {\Delta}\in(-\infty,1]) on two kinds of diamond-type hierarchical (DH) lattices with fractal…
We present numerical evidence for the fact that the damage spreading transition in the Domany-Kinzel automaton found by Martins {\it et al.} is in the same universality class as directed percolation. We conjecture that also other damage…
We present results from lattice simulations of a monolayer graphene model at non-zero temperature. At low temperatures for sufficiently strong coupling the model develops an excitonic condensate of particle-hole pairs corresponding to an…
We investigate bond- and site-percolation models on several two-dimensional lattices numerically, by means of transfer-matrix calculations and Monte Carlo simulations. The lattices include the square, triangular, honeycomb kagome and diced…
A one dimensional network on which there are long range bonds at lattice distances $l>1$ with the probability $P(l) \propto l^{-\delta}$ has been taken under consideration. We investigate the critical behavior of the Ising model on such a…
The Dyson hierarchical one-dimensional Ising model of parameter $\sigma>0$ contains long-ranged ferromagnetic couplings decaying as $1/r^{1+\sigma}$ in terms of the distance $r$. We study the stochastic dynamics near zero-temperature via…
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 investigate the behavior of the Ising model on two connected Barabasi-Albert scale-free networks. We extend previous analysis and show that a first order temperature-driven phase transition occurs in such system. The transition between…
We consider the directed percolation process as a prototype of systems displaying a nonequilibrium phase transition into an absorbing state. The model is in a critical state when the activation probability is adjusted at some precise value…
Phase transition of the classical Ising model on the Sierpi\'{n}ski carpet, which has the fractal dimension $\log_3^{~} 8 \approx 1.8927$, is studied by an adapted variant of the higher-order tensor renormalization group method. The…
Discontinuous percolation transitions and the associated tricritical points are manifest in a wide range of both equilibrium and non-equilibrium cooperative phenomena. To demonstrate this, we present and relate the continuous and first…
In this paper we study the Poisson stick model in two dimensional hyperbolic space $\mathbb{H}^2,$ where the sticks all have length $L.$ Typically, percolation models in hyperbolic space undergo two phase transitions as the intensity…