Related papers: Percolation and Cluster Formalism in Continuous Sp…
We present cluster Monte Carlo algorithms for the $XYZ$ quantum spin models. In the special case of $S=1/2$, the new algorithm can be viewed as a cluster algorithm for the 8-vertex model. As an example, we study the $S=1/2$ $XY$ model in…
Although well described by mean-field theory in the thermodynamic limit, scaling has long been puzzling for finite systems in high dimensions. This raised questions about the efficacy of the renormalization group and foundational concepts…
The review is a brief description of the state of problems in percolation theory and their numerous applications, which are analyzed on base of interesting papers published in the last 15-20 years. At the submitted papers are studied both…
Quantum periodic cluster methods for strongly correlated electron systems are reformulated and developed. The reformulation and development are based on a canonical transformation which periodizes the fermions in the cluster space. The…
The magnetically ordered, low temperature phase of Ising ferro- magnets is manifested within the associated Fortuin-Kasteleyn (FK) random cluster representation by the occurrence of a single positive density percolating cluster. In this…
The theoretical basis of continuum percolation has changed greatly since its beginning as little more than an analogy with lattice systems. Nevertheless, there is yet no comprehensive theory of this field. A basis for such a theory is…
An order parameter, termed the maximal row correlation, is proposed for classical spin systems. Monte Carlo simulations on various Potts models suggest that this order parameter is applicable to a broad range of spin systems, including…
Magnetic ordering at low temperature for Ising ferromagnets manifests itself within the associated Fortuin-Kasteleyn (FK) random cluster representation as the occurrence of a single positive density percolating network. In this paper we…
The cluster synchronization is a very important characteristic for the higher harmonic coupling Kuramoto system. A novel transformation is provided, and it gives cluster synchronization by the periodic properties of the density function.…
In cluster tomography, we propose measuring the number of clusters $N$ intersected by a line segment of length $\ell$ across a finite sample. As expected, the leading order of $N(\ell)$ scales as $a\ell$, where $a$ depends on microscopic…
We introduce a simple lattice model in which percolation is constructed on top of critical percolation clusters, and show that it can be repeated recursively any number $n$ of generations. In two dimensions, we determine the percolation…
Cluster algorithms for classical and quantum spin systems are discussed. In particular, the cluster algorithm is applied to classical O(N) lattice actions containing interactions of more than two spins. The performance of the multi-cluster…
We discuss a new cluster representation for the internal energy and the specific heat of the d-dimensional Ising model, obtained by studying the percolation mapping of an Ising model with an arbitrary set of antiferromagnetic links. Such a…
We develop a full theoretical approach to clustering in complex networks. A key concept is introduced, the edge multiplicity, that measures the number of triangles passing through an edge. This quantity extends the clustering coefficient in…
We introduce the concept of soliton clusters -- multi-soliton bound states in a homogeneous bulk optical medium, and reveal a key physical mechanism for their stabilization associated with a staircase-like phase distribution that induces a…
We discussed hierarchies and rescaling rule of the self similar transformations in Ising models, and define a fractal dimension of an ordered cluster, which minimum corresponds to a fixed point of the transformations. By the fractal…
We study the geometric properties of a system initially in equilibrium at a critical point that is suddenly quenched to another critical point and subsequently evolves towards the new equilibrium state. We focus on the bidimensional Ising…
Multi-particle form factors of local operators in integrable models in two dimensions seem to have the property that they factorize when one subset of the particles in the external states are boosted by a large rapidity with respect to the…
Percolation is a paradigmatic model in disordered systems and has been applied to various natural phenomena. The percolation transition is known as one of the most robust continuous transitions. However, recent extensive studies have…
A theoretical and numerically study of dynamical properties in the sol-gel transition is presented. In particular, the complex phenomenology observed experimentally and numerically in gelling systems is reproduced in the framework of…