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A theoretical model for fractal growth of DLA-clusters in two- and three-dimensional Euclidean space is proposed. This model allows to study some statistical properties of growing clusters in two different situations: in the static case…
We consider the critical behavior at an interface which separates two semi-infinite subsystems belonging to different universality classes, thus having different set of critical exponents, but having a common transition temperature. We…
In a recent paper, we considered the effects of the torus lattice topology on the two-point connectivity of $Q-$ Potts clusters. These effects are universal and probe non-trivial structure constants of the theory. We complete here this work…
We establish an intriguing connection between geometry and thermodynamics in the critical q-state Potts model on two-dimensional lattices, using the q-state bond-correlated percolation model (QBCPM) representation. We find that the number…
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…
We propose a novel finite size scaling analysis for percolation transition observed in complex networks. While it is known that cooperative systems in growing networks often undergo an infinite order transition with inverted…
In a statistical cluster or loop model such as percolation, or more generally the Potts models or O(n) models, a pinch point is a single bulk point where several distinct clusters or loops touch. In a polygon P harboring such a model in its…
Through the Monte Carlo simulation of the three-dimensional, three-state Potts model, which is a paradigm of finite-temperature pure gauge QCD, we study the fluctuations of generalized susceptibilities near the temperatures of external…
We numerically investigate the heterogeneity in cluster sizes in the two-dimensional Ising model and verify its scaling form recently proposed in the context of percolation problems [Phys. Rev. E 84, 010101(R) (2011)]. The scaling exponents…
The critical behaviour of correlation functions near a boundary is modified from that in the bulk. When the boundary is smooth this is known to be characterised by the surface scaling dimension $\xt$. We consider the case when the boundary…
We present a numerical study of 2D random-bond Potts ferromagnets. The model is studied both below and above the critical value $Q_c=4$ which discriminates between second and first-order transitions in the pure system. Two geometries are…
The multifractal properties of electronic eigenstates at the metal-insulator transition of a two-dimensional disordered tight-binding model with spin-orbit interaction are investigated numerically. The correlation dimensions of the spectral…
We use scale invariant scattering theory to exactly determine the renormalization group fixed points of a $q$-state Potts model coupled to an $r$-state Potts model in two dimensions. For integer values of $q$ and $r$ the fixed point…
We apply a simple analytical criterion for locating critical temperatures to Potts models on square and triangular lattices. In the self-dual case, i.e. on the square lattice we reproduce known exact values of the critical temperature and…
We study the three-point correlation function of the backbone in the two-dimensional $Q$-state Potts model using the Fortuin--Kasteleyn (FK) representation. The backbone is defined as the biconnected skeleton of an FK cluster after removing…
The two-dimensional site percolation problem is studied by transfer-matrix methods on finite-width strips with free boundary conditions. The relationship between correlation-length amplitudes and critical indices, predicted by conformal…
A cluster algorithm is presented for the simulation of the q-state Potts models in which the number of spins is conserved in each state. The algorithm constructs Fortuin-Kasteleyn cluster configurations from spin configurations, in a way…
We present selfdual manifolds for coupled Potts models on the triangular lattice. We exploit two different techniques: duality followed by decimation, and mapping to a related loop model. The latter technique is found to be superior, and it…
We study the fractal properties of depth-first search (DFS) paths in critical configurations of statistical physics models, including the two-dimensional $O(n)$ loop model for various $n$, and bond percolation in dimensions $d = 2$ to $6$.…
Critical properties of hulls of directed spiral percolation (DSP) clusters are studied on the square and triangular lattices in two dimensions (2D). The hull fractal dimension ($d_H$) and some of the critical exponents associated with…