相关论文: Geometrical properties of parafermionic spin model…

Suitable cluster definitions have allowed researchers to describe many ordering transitions in spin systems as geometric phenomena related to percolation. For spin glasses and some other systems with quenched disorder, however, such a…

The Fortuin-Kasteleyn mapping between the Ising model and the site-bond correlated percolation model is shown to be only one of an infinite class of exact mappings. These new cluster representations are a result of "renormalized"…

The concept of z-scaling previously developed for analysis of inclusive reactions in proton-proton collisions is applied for description of processes with polarized particles. Hypothesis of self-similarity of the proton spin structure is…

The lattice spin model, with nearest neighbor ferromagnetic exchange and long range dipolar interaction, is studied by the method of time series for observables based on cluster configurations and associated partitions, such as Shannon…

The conjectured exact percolation thresholds of the Fortuin-Kasteleyn cluster for the +-J Ising spin glass model are theoretically shown based on a conjecture. It is pointed out that the percolation transition of the Fortuin-Kasteleyn…

We consider geometrical clusters (i.e. domains of parallel spins) in the square lattice random field Ising model by varying the strength of the Gaussian random field, $\Delta$. In agreement with the conclusion of previous investigation…

In this paper we lay special stress on analyzing the topological properties of the lattice systems and try to ovoid the conventional ways to calculate the critical points. Only those clusters with finite sizes can execute the self similar…

The fractal dimensions of polymer chains and high-temperature graphs in the Ising model both in three dimension are determined using the conformal bootstrap applied for the continuation of the $O(N)$ models from $N=1$ (Ising model) to $N=0$…

We study the dynamical properties of the fully frustrated Ising model. Due to the absence of disorder the model, contrary to spin glass, does not exhibit any Griffiths phase, which has been associated to non-exponential relaxation dynamics.…

After fifty years of lattice gauge theories (LGTs), the nature of the transition between their topological phases (confinement/deconfinement) remains challenging due to the absence of a local order parameter. In this work, we conduct a…

Scanning probes reveal complex, inhomogeneous patterns on the surface of many condensed matter systems. In some cases, the patterns form self-similar, fractal geometric clusters. In this paper, we advance the theory of criticality as it…

The fractal structure of directed percolation clusters, grown at the percolation threshold inside parabolic-like systems, is studied in two dimensions via Monte Carlo simulations. With a free surface at y=\pm Cx^k and a dynamical exponent…

We have considered clusters of like spin in the Q-Potts model, the spin Potts clusters. Using Monte Carlo simulations, we studied these clusters on a square lattice with periodic boundary conditions for values of Q in [1,4]. We continue the…

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…

We present a large class of three-dimensional spin models that possess topological order with stability against local perturbations, but are beyond description of topological quantum field theory. Conventional topological spin liquids, on a…

Fractons are topological quasiparticles with limited mobility. While there exists a variety of models hosting these excitations, typical fracton systems require rather complicated many-particle interactions. Here, we discuss fracton…

A geometric approach to critical fluctuations of a nonequilibrium model is reported. The two-dimensional majority vote model was investigated by Monte Carlo simulations on square lattices of various sizes and a detailed scaling analysis of…

We consider the effects of spatial correlations in a two-dimensional site percolation model. By generalizing the Newman-Ziff Monte Carlo algorithm to include spatial correlations, percolation thresholds and fractal dimensions of percolation…

For the Ising model, the spin magnetization transition is equivalent to the percolation transition of Fortuin-Kasteleyn clusters; this result remains valid also for the conventional continuous spin Ising model. The investigation of more…

A measure of cluster size heterogeneity ($H$), introduced by Lee et al [Phys. Rev. E {\bf 84}, 020101 (2011)] in the context of explosive percolation, was recently applied to random percolation and to domains of parallel spins in the Ising…