Related papers: Percolation and Magnetization for Generalized Cont…
Effective theories are helpful tools to gain an intuitive insight into phenomena governed by complex laws. In this work we show by means of Monte Carlo simulations that Z(2) spin models with only spin-spin interactions approximate rather…
The fractal structure and scaling properties of a 2d slice of the 3d Ising model is studied using Monte Carlo techniques. The percolation transition of geometric spin (GS) clusters is found to occur at the Curie point, reflecting the…
Continuous phase transitions in spin systems can be formulated as percolation of suitably defined clusters. We review this equivalence and then discuss how in a similar way, the color deconfinement transition in SU(2) gauge theory can be…
In the ordered phase of the 3D Ising model, minority spin clusters are surrounded by a boundary of dual plaquettes. As the temperature is raised, these spin clusters become more numerous, and it is found that eventually their boundaries…
The spontaneous symmetry breaking in the Ising model can be equivalently described in terms of percolation of Wolff clusters. In O(n) spin models similar clusters can be built in a general way, and they are currently used to update these…
Based on the connection between the Ising model and a correlated percolation model, we calculate the distribution function for the fraction ($c$) of lattice sites in percolating clusters in subgraphs with $n$ percolating clusters, $f_n(c)$,…
We consider a zero-field Ising model defined on a quasiperiodic graph, the so-called Labyrinth tiling. Exact information about the critical behaviour is obtained from duality arguments and the subclass of models which yield commuting…
In this paper we consider an approach, which allows researching a processes of order-disorder transition in various systems (with any distribution of the exchange integrals signs) in the frame of Ising model. A new order parameters, which…
The Fortuin-Kasteleyn (FK) random cluster model, which can be exactly mapped from the $q$-state Potts spin model, is a correlated bond percolation model. By extensive Monte Carlo simulations, we study the FK bond representation of the…
We establish that the Fourier modes of the magnetization serve as the dynamical eigenmodes for the two-dimensional Ising model at the critical temperature with local spin-exchange moves, i.e., Kawasaki dynamics. We obtain the dynamical…
The universality class of the dynamic magnetisation-reversal transition, induced by a competing field pulse, in an Ising model on a square lattice, below its static ordering temperature, is studied here using Monte Carlo simulations. Fourth…
Ashkin-Teller model is a two-layer lattice model where spins in each layer interact ferromagnetically with strength $J$, and the spin-dipoles (product of spins) interact with neighbors with strength $\lambda.$ The model exhibits…
The percolation, Ising, and O($n$) models constitute fundamental systems in statistical and condensed matter physics. For short-range-interacting cases, the nature of their phase transitions is well established by renormalization-group…
The critical behaviour of several spin models can be simply described as percolation of some suitably defined clusters, or droplets: the onset of the geometrical transition coincides with the critical point and the percolation exponents are…
We show that deconfinement in SU(2) gauge theory can be described by the percolation of site-bond clusters of like-sign Polyakov loops. In particular, we find that in 2+1 dimensions the percolation variables coincide with those of the…
The couplings between the Ising model and its graphical representations, the random-cluster, random current and loop $\mathrm{O}(1)$ models, are put on common footing through a generalization of the Swendsen-Wang-Edwards-Sokal coupling. A…
The fractal dimensions and the percolation exponents of the geometrical spin clusters of like sign at criticality, are obtained numerically for an Ising model with temperature-dependent annealed bond dilution, also known as the thermalized…
We investigate the percolation behavior of Fortuin-Kasteleyn--type clusters in the spin-$1/2$ Baxter--Wu model with three-spin interactions on a triangular lattice. The considered clusters are constructed by randomly freezing one of the…
It was pointed out by de Arcangelis et al. [Europhys. Lett. 14 (1991), 515] that the correct understanding of the percolation phenomenon of the Fortuin-Kasteleyn cluster in the Edwards-Anderson model is important since a dynamical…
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…