Related papers: Dynamical replica analysis of disordered Ising spi…
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…
We consider the ferromagnetic Ising model with Glauber spin flip dynamics in one dimension. The external magnetic field vanishes and the couplings are i.i.d. random variables. If their distribution has compact support, the disorder averaged…
Spin glasses, generally defined as disordered systems with randomized competing interactions, are a widely investigated complex system. Theoretical models describing spin glasses are broadly used in other complex systems, such as those…
We use the cavity method to study parallel dynamics of disordered Ising models on a graph. In particular, we derive a set of recursive equations in single site probabilities of paths propagating along the edges of the graph. These equations…
Extensive Monte Carlo simulations are performed on a two-dimensional random field Ising model. The purpose of the present work is to study the disorder-induced changes in the properties of disordered spin systems. The time evolution of the…
The Ising model on networks plays a fundamental role as a testing ground for understanding cooperative phenomena in complex systems. Here we solve the synchronous dynamics of the Ising model on random graphs with an arbitrary degree…
We consider ferromagnetic Ising models on graphs that converge locally to trees. Examples include random regular graphs with bounded degree and uniformly random graphs with bounded average degree. We prove that the "cavity" prediction for…
Non-equilibrium dynamics of classical random Ising spin chains are studied using asymptotically exact real space renormalization group. Specifically the random field Ising model with and without an applied field (and the Ising spin glass…
The Ising spin glass in two dimensions exhibits rich behavior with subtle differences in the scaling for different coupling distributions. We use recently developed mappings to graph-theoretic problems together with highly efficient…
Consider a collection of random variables attached to the vertices of a graph. The reconstruction problem requires to estimate one of them given `far away' observations. Several theoretical results (and simple algorithms) are available when…
A zero temperature dynamics of Ising spin glasses and ferromagnets on random graphs of finite connectivity is considered, like granular media these systems have an extensive entropy of metastable states. We consider the problem of what…
We address the issue of universality in two-dimensional disordered Ising systems, by considering long, finite-width strips of ferromagnetic Ising spins with randomly distributed couplings. We calculate the free energy and spin-spin…
We start from the Theory of Random Point Processes to derive n-point coupled master equations describing the continuous dynamics of discrete variables in random graphs. These equations constitute a hierarchical set of approximations that…
We present a new method to solve the dynamics of disordered spin systems on finite time-scales. It involves a closed driven diffusion equation for the joint spin-field distribution, with time-dependent coefficients described by a dynamical…
We address the question of geometrical as well as energetic properties of local excitations in mean field Ising spin glasses. We study analytically the Random Energy Model and numerically a dilute mean field model, first on tree-like…
We investigate analytically and numerically an Ising spin model with ferromagnetic coupling defined on random graphs corresponding to Feynman diagrams of a $\phi^q$ field theory, which exhibits a mean field phase transition. We explicitly…
We derive the analytical expression for the first finite size correction to the average free energy of disordered Ising models on random regular graphs. The formula can be physically interpreted as a weighted sum over all non…
The p-spin spin-glass model has been studied extensively at mean-field level because of the insights which it provides into the mode-coupling approach to structural glasses and the nature of the glass transition. We demonstrate explicitly…
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…
The thermodynamics of the infinite-range Ising spin glass with p-spin interactions in the presence of an external magnetic field h is investigated analytically using the replica method. We give emphasis to the analysis of the transition…