Related papers: Metastable configurations of spin models on random…
Dynamical systems, that are used to model power grids, the brain, and other physical systems, can exhibit coexisting stable states known as attractors. A powerful tool to understand such systems, as well as to better predict when they may…
We study networks of coupled bistable elastic elements, recently proposed as a model for crumpled thin sheets. The networks are poised on the verge of a localized instability, and the model allows unique access to both local and global…
In this paper we study the phase diagram of two Ising planes coupled by a standard spin-spin interaction with bond randomness in each plane. The whole phase diagram is analyzed by help of Monte Carlo simulations and field theory arguments.
In this study the magnetization phenomenon has been investigated as a behavior of interacting elementary moments ensemble, with the help of Ising model [1] in the frame of non-extensive statistical mechanics. To investigate the physical…
A nonuniform extension of the Glauber model on a one-dimensional lattice with boundaries is investigated. Based on detailed balance, reaction rates are proposed for the system. The static behavior of the system is investigated. It is shown…
We examine the issue of stability of probability in reasoning about complex systems with uncertainty in structure. Normally, propositions are viewed as probability functions on an abstract random graph where it is implicitly assumed that…
Random fields of scales result when the class of musical scales is thought as a set of sites, and a site can be in one of two possible states (or spins): On or Off. We present a flexible simulated annealing model that produces generic…
We investigate the application of the line-graph operator to one-dimensional spin models with periodic boundary conditions. The spins (or interactions) in the original spin structure become the interactions (or spins) in the resulting spin…
By varying a parameter of a one-dimensional piecewise smooth map, stable periodic orbits are observed. In this paper, complete analytic characterization of these stable periodic orbits is obtained. An interesting relationship between the…
The mean number <N> of metastable states in higher order short-range spin glasses is estimated analytically using a variational method introduced by Tanaka and Edwards for very large coordination numbers. For lattices with small…
Configurations are necklaces with prescribed numbers of red and black beads. Among all possible configurations, the regular one plays an important role in many applications. In this paper, several aspects of regular configurations are…
We study analytically M-spin-flip stable states in disordered short-ranged Ising models (spin glasses and ferromagnets) in all dimensions and for all M. Our approach is primarily dynamical and is based on the convergence of a…
By applying a recently proposed mapping, we derive exactly the upper phase boundary of several Ising spin glass models defined over static graphs and random graphs, generalizing some known results and providing new ones.
We explore the cooperative behaviour and phase transitions of interacting networks by studying a simplified model consisting of Ising spins placed on the nodes of two coupled Erd\"os-R\'enyi random graphs. We derive analytical expressions…
We use a random pinning procedure to investigate stable glassy states associated with large deviations of the activity in a model glass-former. We pin particles both from active (equilibrium) configurations and from stable (inactive) glassy…
Ordering at arbitrarily high temperature - entropic order - has been argued to take place in a class of generalized Ising models parameterised by a real interaction parameter $p$ when $p\ge 1$. We give a rigorous proof of this conjecture.…
Synchronization in systems of coupled Kuramoto oscillators may depend on their natural frequencies, coupling, and underlying networks. In this paper, we reduce the alternatives to only one by considering identical oscillators where the only…
We analyse the steady state regime of a one dimensional Ising model under a tapping dynamics recently introduced by analogy with the dynamics of mechanically perturbed granular media. The idea that the steady state regime may be described…
We present a linear stability analysis of stationary states (or fixed points) in large dynamical systems defined on random directed graphs with a prescribed distribution of indegrees and outdegrees. We obtain two remarkable results for such…
As countless examples show, it can be fruitful to study a sequence of complicated objects all at once via the formalism of generating functions. We apply this point of view to the homology and combinatorics of orbit configuration spaces:…