Related papers: Parallel dynamics of disordered Ising spin systems…
Diagonalizability plays an important role in the analysis and design of multivariable systems. A structured matrix is called structurally diagonalizable if almost all of its numerical realizations, obtained by assigning real values to its…
We study the problem of deterministic approximate counting of matchings and independent sets in graphs of bounded connective constant. More generally, we consider the problem of evaluating the partition functions of the monomer-dimer model…
We study a minimal model of disordered systems, the random field Ising model (RFIM) on a generalized Petersen Graph, GP(N,k). This graph has a connected inner and outer loop, where both the loops consist of N nodes constituting a total of…
Suppose we are given a system of coupled oscillators on an unknown graph along with the trajectory of the system during some period. Can we predict whether the system will eventually synchronize? Even with a known underlying graph…
The known Pfaffian structure of the boundary spin correlations, and more generally order-disorder correlation functions, is given a new explanation through simple topological considerations within the model's random current representation.…
We study a disordered network of bistable bonds subjected to periodic strain. The model is inspired by experiments on crumpled sheets and it features behaviors associated with glasses, including a complex energy landscape, memories, and…
The application of the collective variables method to the study of the behaviour of nonuniversal characteristics of the system in the critical region is illustrated by an example of the order parameter. Explicit expressions for the order…
Using analytic and numerical methods, we study a $2d$ Hamiltonian model of interacting particles carrying ferro-magnetically coupled continuous spins which are also locally coupled to their own velocities. This model has been characterised…
A general approach for the description of spin systems on hierarchial lattices with coordination number $q$ as a dynamical variable is proposed. The ferromagnetic Ising model on the Bethe lattice was studied as a simple example…
We perform a numerical investigation of the \emph{shaken dynamics}, a parallel Markovian dynamics for spin systems with local interaction and whose transition probabilities depend on two parameters, $q$ and $J$, that tune the geometry of…
We investigate the dynamics of an initially disentangled Gaussian state on a general finite symmetric graph. As concrete examples we obtain properties of this dynamics on mean field graphs of arbitrary sizes. In the same way that chains can…
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…
Dynamical Ising machines are based on continuous dynamical systems evolving from a generic initial state to a state strongly related to the ground state of the classical Ising model on a graph. Reaching the ground state is equivalent to…
Disordered mechanical systems with high connectivity represent a limit opposite to the more familiar case of disordered crystals. Individual ions in a crystal are subjected essentially to nearest-neighbor interactions. In contrast, the…
This paper addresses questions regarding controllability for `generic parameter' dynamical systems, i.e. the question whether a dynamical system is `structurally controllable'. Unlike conventional methods that deal with structural…
We apply a real-space block renormalization group approach to study the critical properties of the random transverse-field Ising spin chain with multispin interactions. First we recover the known properties of the traditional model with…
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…
We theoretically study magnetization relaxation of Ising spins distributed randomly in a $d$-dimension homogeneous and Gaussian profile under a soft-core two-body interaction potential $\propto1/[1+(r/R_c)^\alpha]$ ($\alpha\ge d$), where…
Synchrony is one of the most common dynamical states emerging on networks. The speed of convergence towards synchrony provides a fundamental collective time scale for synchronizing systems. Here we study the asymptotic synchronization times…
We consider an infinite system of coupled stochastic differential equations (SDE) describing dynamics of the following infinite particle system. Each partricle is characterised by its position $x\in \mathbb{R}^{d}$ and internal parameter…