Related papers: Graphical representations and cluster algorithms f…
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 critical and multicritical behavior of the simple cubic Ising model with nearest-neighbor, next-nearest-neighbor and plaquette interactions is studied using the cube and star-cube approximations of the cluster variation method and the…
We study the dynamical percolation transition of the geometrical clusters in the two-dimensional Ising model when it is subjected to a pulsed field below the critical temperature. The critical exponents are independent of the temperature…
Important graph mining problems such as Clustering are computationally demanding. To significantly accelerate these problems, we propose ProbGraph: a graph representation that enables simple and fast approximate parallel graph mining with…
Graph clustering is an important algorithmic technique for analysing massive graphs, and has been widely applied in many research fields of data science. While the objective of most graph clustering algorithms is to find a vertex set of low…
Graph clustering is a fundamental technique in data analysis with applications in many different fields. While there is a large body of work on clustering undirected graphs, the problem of clustering directed graphs is much less understood.…
The random field Ising model with Gaussian disorder is studied using a new Monte Carlo algorithm. The algorithm combines the advantanges of the replica exchange method and the two-replica cluster method and is much more efficient than the…
We present a detailed study of the phase diagram of the Ising model in random graphs with arbitrary degree distribution. By using the replica method we compute exactly the value of the critical temperature and the associated critical…
We study the 2d-Ising model defined on finite boxes at temperatures that are below but very close from the critical point. When the temperature approaches the critical point and the size of the box grows fast enough, we establish large…
Hierarchical graph clustering is a common technique to reveal the multi-scale structure of complex networks. We propose a novel metric for assessing the quality of a hierarchical clustering. This metric reflects the ability to reconstruct…
This paper is devoted to computational algorithms designed to describe the classical Ising magnet in some specific cases when an additional macroscopic restriction in form of constant charge density exists in the system. We developed and…
We study the approximability of computing the partition function for ferromagnetic two-state spin systems. The remarkable algorithm by Jerrum and Sinclair showed that there is a fully polynomial-time randomized approximation scheme (FPRAS)…
We obtain an explicit realization of all the primary fields of the Ising model in terms of a conformal field theory of constrained fermions. The four-point correlators of the energy, order and disorder operators are explicitly calculated.
Recent numerical simulations indicate that several different equilibrium glass transitions may be characterized by diverging correlation lengths, and that these divergences are described by a non-mean-field, Ising-like, critical exponent. I…
We have studied numerically the appearance of multiscaling behavior in the three-dimensional ferromagnetic Ising site diluted model, in the form of a multifractal distribution of the decay exponents for the spatial correlation functions at…
We apply a new updating algorithm scheme to investigate the critical behavior of the two-dimensional ferromagnetic Ising model on a triangular lattice with nearest neighbour interactions. The transition is examined by generating accurate…
Ising spin-glass systems with long-range interactions ($J(r)\sim r^{-\sigma}$) are considered. A numerical study of the critical behaviour is presented in the non-mean-field region together with an analysis of the probability distribution…
In an artificial 3D percolation nano medium, the clusters filled by the Ising magnets give rise to a topologically nontrivial magnetic structure, leading to new features of the ferromagnetic phase transition without an external magnetic…
The near-critical unitary dynamics of quantum Ising spin chains in transversal and longitudinal magnetic fields is studied using an artificial neural network representation of the wave function. A focus is set on strong spatial correlations…
We study a Hamiltonian system describing a three-spin-1/2 cluster-like interaction competing with an Ising-like anti-ferromagnetic interaction. We compute free energy, spin correlation functions and entanglement both in the ground and in…