Related papers: Magnetic models on various topologies
Site diluted spin-1/2 Ising and spin-1 Blume Capel (BC) models in the presence of transverse field interactions are examined by introducing an effective-field approximation that takes into account the multi-site correlations in the cluster…
Spatial correlations - bubbles, domain walls, etc. - can best be studied by concentrating on the degrees of freedom most relevant to the problem. For the finite temperature confinement transition, I integrate out all gauge degrees of…
The Ising model on ``thin'' graphs (standard Feynman diagrams) displays several interesting properties. For ferromagnetic couplings there is a mean field phase transition at the corresponding Bethe lattice transition point. For…
One-dimensional superlattices with periodic spatial modulations of onsite potentials or tunneling coefficients can exhibit a variety of properties associated with topology or symmetry. Recent developments of ring-shaped optical lattices…
A review is given on some recent developments in the theory of the Ising model in a random field. This model is a good representation of a large number of impure materials. After a short repetition of earlier arguments, which prove the…
We study the small-world networks recently introduced by Watts and Strogatz [Nature {\bf 393}, 440 (1998)], using analytical as well as numerical tools. We characterize the geometrical properties resulting from the coexistence of a local…
Although two-dimensional periodic structures have functioned as the primary platform for exploring topological phenomena, recent advances have substantially expanded this research boundary to include more intricate, aperiodic structures:…
Given discrete degrees of freedom (spins) on a graph interacting via an energy function, what can be said about the energy local minima and associated inherent structures? Using the lid algorithm in the context of a spin glass energy…
We consider Ising model on edge-dual of uncorrelated random networks with arbitrary degree distribution. These networks have a finite clustering in the thermodynamic limit. High and low temperature expansions of Ising model on the edge-dual…
Recent efforts in lattice evaluation of the topological susceptibility had shown that at high temperatures it is given by well-separated instantons (even in QCD with light fermions, where those are highly suppressed). Recent development of…
We introduce the notion of topological electronic states on random lattices in non-integer dimensions. By considering a class $D$ model on critical percolation clusters embedded in two dimensions, we demonstrate that these topological…
Frames, or lattices consisting of mass points connected by rigid bonds or central force springs, are important model constructs that have applications in such diverse fields as structural engineering, architecture, and materials science.…
A one dimensional kinetic Ising model at a finite temperature on a semi-infinite lattice with time varying boundary spins is considered. Exact expressions for the expectation values of the spin at each site are obtained, in terms of the…
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…
We analyze changes in the thermodynamic properties of a spin system when it passes from the classical two-dimensional Ising model to the spin glass model, where spin-spin interactions are random in their values and signs. Formally, the…
A certain class of one-dimensional classical lattice models is considered. Using the method of abstract harmonic analysis explicit thermostatic properties of such models are derived. In particular, we discuss the low-temperature behavior of…
Thermodynamics of itinerant magnets is studied using a classical model with one parameter characterizing the degree of itinerancy. Monte Carlo simulations for bcc and fcc lattices are compared with the mean-field approximation and with the…
We discuss the use of a ferromagnetic spin model on a random graph to model granular compaction. A multi-spin interaction is used to capture the competition between local and global satisfaction of constraints characteristic for geometric…
The purpose of this manuscript is to review my recent activity on three main research topics. The first concerns the nature of low temperature amorphous solids and their relation with the spin glass transition in a magnetic field. This is…
Real-world networks, e.g. the social relations or world-wide-web graphs, exhibit both small-world and scale-free behaviour. We interpret lattice triangulations as planar graphs by identifying triangulation vertices with graph nodes and…