Related papers: The Random-Cluster Model
A new class of probabilistic models for cascading failure propagation in interconnected systems is proposed. The models take into account important characteristics of real systems that are not considered in existing generic approaches.…
Coordination processes in complex systems can be related to the problem of collective ordering in networks, many of which have modular organization. Investigating the order-disorder transition for Ising spins on modular random networks,…
The ground-state of an infinite-range Potts glass-type model with +/- J bonds and unrestricted number of states is used to investigate coalition formation. As a function of the q probability of +J bonds in the system it is found that the r…
In two space dimensions, the percolation point of the pure-site clusters of the Ising model coincides with the critical point T_c of the thermal transition and the percolation exponents belong to a special universality class. By introducing…
Cluster randomized trials (CRTs) offer a practical alternative for addressing logistical challenges and ensuring feasibility in community health, education, and prevention studies, even though randomized controlled trials are considered the…
We consider the Potts model on a two-dimensional periodic rectangular lattice with general coupling constants $J_{ij}>0$, where $i,j\in\{1,2,3\}$ are the possible spin values (or colors). The resulting energy landscape is thus significantly…
It is demonstrated that the scaled order parameter for ferromagnetic Ising and three-state Potts chains with inverse-square interactions exhibits a universal critical jump, in analogy with the superfluid density in helium films.…
We investigate the effect of phase randomness in Ising-type quantum networks. These networks model a large class of physical systems. They describe micro- and nanostructures or arrays of optical elements such as beam splitters…
We have provided a concise introduction to the Ising model as one of the most important models in statistical mechanics and in studying the phenomenon of phase transition. The required theoretical background and derivation of the…
Critical behaviour of a nearly critical system, subjected to vivid turbulent mixing, is studied by means of the field theoretic renormalization group. Namely, relaxational stochastic dynamics of a non-conserved order parameter of the…
This study contributes to the body of work on instabilities in the homogeneous cooling system focusing on clustering in the multiphase gas-particle system. The critical system size for the onset of instability, $L^*_c$, is studied via three…
The problem of pattern formation in a generic two species reaction--diffusion model is studied, under the hypothesis that only one species can diffuse. For such a system, the classical Turing instability cannot take place. At variance, by…
Deterministic simulations of the rate equations governing cluster dynamics in materials are limited by the number of equations to integrate. Stochastic simulations are limited by the high frequency of certain events. We propose a coupling…
In the past few years co-clustering has emerged as an important data mining tool for two way data analysis. Co-clustering is more advantageous over traditional one dimensional clustering in many ways such as, ability to find highly…
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…
Quantum cluster theories are a set of approaches for the theory of correlated and disordered lattice systems, which treat correlations within the cluster explicitly, and correlations at longer length scales either perturbatively or within a…
Critical points and singularities are encountered in the study of critical phenomena in probability and physics. We present recent results concerning the values of such critical points and the nature of the singularities for two prominent…
We investigate a perturbatively renormalizable $S_{q}$ invariant model with $N=q-1$ scalar field components below the upper critical dimension $d_c=\frac{10}{3}$. Our results hint at the existence of multicritical generalizations of the…
Using the concept of finite-size scaling, Monte Carlo calculations of various models have become a very useful tool for the study of critical phenomena, with the system linear dimension as a variable. As an example, several recent studies…
Machine-learning (ML) models trained on Ising spin configurations have demonstrated surprising effectiveness in classifying phases of Potts models, even when processing severely reduced representations that retain only two spin states. To…