Related papers: The Ising antiferromagnet and max cut on random re…
The effects of random magnetic fields are considered in an Ising spin-glass model defined in the limit of infinite-range interactions. The probability distribution for the random magnetic fields is a double Gaussian, which consists of two…
We consider an Ising model on the Cayley tree $\Gamma_k$ of arbitrary order $k\ge1$ with three spin species of values $(\tfrac12,1,\tfrac32)$ distributed deterministically with period three along the generations. Within the framework of…
Ising machines (IM) have recently been proposed as unconventional hardware-based computation accelerators for solving NP-hard problems. In this work, we present a model for a time-multiplexed IM based on the nonlinear oscillations in a…
Motivated by recent experiments on TmB4 (arXiv:0712.1537), we examine the phase diagram of the Shastry-Sutherland antiferromagnet in an applied magnetic field in the limit of strong Ising anisotropy. In classical Ising limit, we demonstrate…
Finding a maximum cut is a fundamental task in many computational settings. Surprisingly, it has been insufficiently studied in the classic distributed settings, where vertices communicate by synchronously sending messages to their…
Markov chains are one of the well-known tools for modeling and analyzing stochastic systems. At the same time, they are used for constructing random walks that can achieve a given stationary distribution. This paper is concerned with…
New advances in experiments on the random-field Ising model, as realized in dilute antiferromagnets, have brought us much closer to a full characterization of the static and dynamic critical behavior of the unusual phase transition in three…
A random-field Ising model that is capable of exhibiting a rich variety of multicritical phenomena, as well as a smearing of such behavior, is investigated. The model consists of an infinite-range-interaction Ising ferromagnet in the…
Using a specially designed Monte Carlo algorithm with directed loops, we investigate the triangular lattice Ising antiferromagnet with coupling beyond nearest neighbour. We show that the first-order transition from the stripe state to the…
Multiplex networks consist of a fixed set of nodes connected by several sets of edges which are generated separately and correspond to different networks ("layers"). Here, a simple variant of the Ising model on multiplex networks with two…
The nonequilibrium dynamic phase transition, in the two dimensional kinetic Ising model in presence of a randomly varying (in time but uniform in space) magnetic field, has been studied both by Monte Carlo simulation and by solving the mean…
Ferromagnetic exponential random graph models (ERGMs) are nonlinear exponential tilts of Erd\H{o}s-R\'enyi models, under which the presence of certain subgraphs such as triangles may be emphasized. These models are mixtures of metastable…
The class of two-spin systems contains several important models, including random independent sets and the Ising model of statistical physics. We show that for both the hard-core (independent set) model and the anti-ferromagnetic Ising…
The antiferromagnetic Ising model in uncorrelated scale-free networks has been studied by means of Monte Carlo simulations. These networks are characterized by a connectivity (or degree) distribution P(k) ~ k^(- gamma). The disorder present…
The identification of phase transition points, beta_c, with the percolation thresholds of suitably defined clusters of spins has proved immensely fruitful in many areas of statistical mechanics. Some time ago Kertesz suggested that such…
We study the community detection problem in the non-uniform hypergraph stochastic block model (HSBM), where hyperedges of varying sizes coexist. This setting captures higher-order and multi-view interactions and raises a fundamental…
We study the phase transition in a face-centered-cubic antiferromagnet with Ising spins as a function of the concentration $p$ of ferromagnetic bonds randomly introduced into the system. Such a model describes the spin-glass phase at strong…
We investigate the unsupervised node classification problem on random hypergraphs under the non-uniform Hypergraph Stochastic Block Model (HSBM) with two equal-sized communities. In this model, edges appear independently with probabilities…
A lot of progress has been made recently in our understanding of the random-field Ising model thanks to large-scale numerical simulations. In particular, it has been shown that, contrary to previous statements: the critical exponents for…
In this paper we study the component structure of random graphs with independence between the edges. Under mild assumptions, we determine whether there is a giant component, and find its asymptotic size when it exists. We assume that the…